May 2025

Class 12 Maths Syllabus At Studit, we understand how important Class 12 Maths is—not just for scoring well in board exams but also for preparing for competitive exams like JEE, CUET, and more. That’s why we’ve put together a clear, chapter-wise index of all the topics covered in the Class 12 CBSE Maths syllabus. This detailed breakdown will help students, parents, and educators track learning progress, revise systematically, and focus on key concepts. Every chapter includes sub-topics that are essential for mastering the subject. Class 12 Maths Chapters and Topics Chapter 1: Relations and Functions Introduction to Relations Types of Relations and Functions Composite Functions and Inverse of a Function Binary Operations Chapter 2: Inverse Trigonometric Functions Basic Concepts Principal Value Branches Properties and Graphs of Inverse Trigonometric Functions Chapter 3: Matrices Definition and Types of Matrices Matrix Operations Transpose, Symmetric & Skew-Symmetric Matrices Elementary Row Operations Invertible Matrices Chapter 4: Determinants Introduction and Properties of Determinants Minors and Cofactors Adjoint and Inverse of a Matrix Application: Area of a Triangle, Solving Linear Equations Chapter 5: Continuity and Differentiability Meaning of Continuity and Differentiability Derivatives of Composite, Implicit, and Parametric Functions Logarithmic and Exponential Functions Second Order Derivatives and Mean Value Theorem Chapter 6: Applications of Derivatives Rate of Change Increasing/Decreasing Functions Tangents and Normals Maxima and Minima Approximation Chapter 7: Integrals Indefinite Integrals Integration Methods: Substitution, By Parts, Partial Fractions Definite Integrals and Properties Fundamental Theorem of Calculus Chapter 8: Application of Integrals Area Under Curves Area Between Two Curves Chapter 9: Differential Equations Introduction and Order/Degree General and Particular Solutions Formation and Solution of Differential Equations Chapter 10: Vector Algebra Vector Basics and Types Vector Operations: Addition, Multiplication Scalar and Vector Products Chapter 11: Three Dimensional Geometry Direction Cosines and Ratios Line and Plane Equations Angles, Distances, and Coplanarity Chapter 12: Linear Programming Introduction to Linear Programming Mathematical Formulation Graphical Method of Solution Chapter 13: Probability Conditional Probability Bayes’ Theorem Random Variables and Distributions Bernoulli Trials and Binomial Distribution Why Use Studit for Class 12 Maths Preparation? At Studit, we believe in smart learning—not just reading but actually understanding. Our platform provides: Topic-wise explanations in a simple and relatable way Practice worksheets and questions after every concept Sample papers and previous years’ questions for exam readiness One-on-one support from expert tutors (available online and offline) Whether you’re revising before the board exams or preparing for entrance tests, Studit ensures that you’re not just solving Maths—you’re understanding it. Frequently Asked Questions (FAQs) – Class 12 Maths at Studit What is the best way to prepare for Class 12 Maths using Studit? At Studit, we recommend a structured approach. Start by understanding each chapter conceptually using our video lessons or one-on-one tutoring. Then move on to solving NCERT problems, sample papers, and previous year questions. Our tutors guide you through each step with personalized support. Can I use Studit to prepare for both board exams and competitive exams like JEE? Yes. Our content and tutoring approach covers both CBSE board exam patterns and the type of questions asked in competitive exams like JEE, CUET, and other entrance tests. We focus on building strong conceptual understanding and problem-solving skills. Are all Class 12 Maths chapters covered on the Studit platform? Absolutely. We provide in-depth coverage of all 13 chapters in the Class 12 Maths syllabus, including all sub-topics. Whether it’s calculus, vectors, or probability, you’ll find clear explanations and practice material for every topic. Can I get personal help if I’m stuck on a topic? Yes. Studit offers personalized home tutoring and online support. If you’re struggling with a topic, our experienced educators will guide you one-on-one to help you fully understand and master it. Do you provide sample papers and worksheets for Class 12 Maths? Yes. We provide topic-wise practice worksheets, sample papers, and past board exam papers to help students build confidence and improve their speed and accuracy. How is Studit different from other online learning platforms? Studit combines the flexibility of online resources with the personal attention of offline/home tutoring. Unlike traditional platforms, we focus on localized, one-on-one support and build a strong learning bond between student and teacher.

Class 11 Maths Syllabus This page provides a complete and detailed Class 11 Maths index, covering all the chapters and subtopics as outlined in the NCERT textbook and prescribed by the CBSE curriculum. At Studit, we have designed this resource to help students clearly understand what they need to learn throughout the academic year, whether they are preparing for school exams or competitive entrance tests like JEE. Understanding mathematics at this level is critical. The concepts introduced in Class 11 lay the groundwork for Class 12 and for various engineering and science entrance exams. This index offers a structured overview that students can use to track their learning and revision more effectively. Overview of Class 11 Maths Units: Sets and Functions Algebra Coordinate Geometry Calculus Mathematical Reasoning Statistics and Probability Unit I: Sets and Functions Chapter 1: Sets Introduction to Sets and their Representations Types of Sets: Empty, Finite, Infinite, Equal Subsets, Power Set, Universal Set Venn Diagrams Operations on Sets: Union, Intersection, Difference, Complement Chapter 2: Relations and Functions Ordered Pairs and Cartesian Products Relations: Definition, Domain, Co-domain, Range Functions as Special Relations Types of Functions: Constant, Identity, Polynomial, Rational, Modulus, Signum, Exponential, Logarithmic, Greatest Integer Operations on Functions Chapter 3: Trigonometric Functions Measurement of Angles in Radians and Degrees Trigonometric Functions Using the Unit Circle Identities: sin²x + cos²x = 1 and others Domain and Range Graphs and Properties of Trigonometric Functions General Solutions to Trigonometric Equations Unit II: Algebra Chapter 4: Principle of Mathematical Induction Concept and Motivation Process of Proof by Induction Simple Applications Chapter 5: Complex Numbers and Quadratic Equations Introduction to Complex Numbers Algebraic Properties and Polar Representation Argand Plane Solving Quadratic Equations with Complex Roots Chapter 6: Linear Inequalities Solutions in One Variable and Two Variables Representation on the Number Line and Graphically Chapter 7: Permutations and Combinations Fundamental Principle of Counting Factorial Notation Derivation of Formulas Real-Life Applications Chapter 8: Binomial Theorem Statement and Proof Pascal’s Triangle General and Middle Terms Simple Applications Chapter 9: Sequences and Series Arithmetic Progression (AP), Arithmetic Mean (AM) Geometric Progression (GP), Geometric Mean (GM) Sum of Series Relationship between AM and GM Unit III: Coordinate Geometry Chapter 10: Straight Lines Basic Concepts of Two-Dimensional Geometry Slope of a Line, Angle Between Lines Various Forms of Line Equations: Point-Slope, Two-Point, Intercept, Normal Form General Equation of a Line Distance from a Point to a Line Chapter 11: Conic Sections Introduction to Circles, Parabolas, Ellipses, Hyperbolas Standard Equations and Properties Degenerated Conic Sections Chapter 12: Introduction to Three-Dimensional Geometry Coordinate Axes and Planes in 3D Coordinates of a Point Distance and Section Formula Unit IV: Calculus Chapter 13: Limits and Derivatives Concept of Limits Derivatives: Definition and First Principles Limits Involving Trigonometric Functions Basic Rules of Differentiation Unit V: Mathematical Reasoning Chapter 14: Mathematical Reasoning Logical Statements and Reasoning Use of Connectives and Validations Understanding Contradictions, Converse, and Contrapositive Unit VI: Statistics and Probability Chapter 15: Statistics Measures of Dispersion: Range, Mean Deviation, Variance, Standard Deviation Comparison of Data Sets Chapter 16: Probability Introduction to Probability Theory Sample Space and Events Axiomatic Approach to Probability Calculating Probabilities of Events and Their Complements Why Choose Studit for Class 11 Maths Preparation? At Studit, we go beyond just listing topics. Our platform offers detailed lessons, practice questions, and conceptual explanations that are easy to understand. Each topic is broken down into manageable parts, so students can study at their own pace while building confidence in their problem-solving skills. Whether you are preparing for school exams or entrance tests like JEE, our resources are designed to guide you through every step. Explore more at Studit and take your preparation to the next level with high-quality learning materials, revision support, and expert-curated resources. Frequently Asked Questions (FAQs) – Class 11 Maths at Studit How many chapters are there in Class 11 Maths? There are 16 chapters in the Class 11 Maths NCERT syllabus, divided across six units: Sets and Functions, Algebra, Coordinate Geometry, Calculus, Mathematical Reasoning, and Statistics & Probability. What is the most important chapter in Class 11 Maths for JEE preparation? Chapters like Trigonometric Functions, Sequences and Series, Complex Numbers, and Limits and Derivatives are crucial for JEE and other competitive exams. A strong understanding of Algebra and Calculus is especially important. Is Class 11 Maths tougher than Class 10 Maths? Yes, students generally find Class 11 Maths more challenging than Class 10. The syllabus introduces abstract concepts like sets, functions, calculus, and complex numbers that require deeper conceptual understanding. Are NCERT books enough for Class 11 Maths? Yes, NCERT is essential and should be your primary resource. For advanced practice, especially for JEE or other entrance exams, you can refer to additional books like RD Sharma, ML Khanna, or coaching modules. What is the best way to study Class 11 Maths? Start with a clear understanding of each concept Practice NCERT examples and exercises thoroughly Solve previous year questions and sample papers Revise regularly to strengthen formulas and theorems Use video lessons or guided tutorials for tough topics How can I score good marks in Class 11 Maths? Focus on conceptual clarity, not just memorizing formulas Practice a variety of problems from each topic Work on your calculation speed and accuracy Take mock tests to improve time management Use a structured timetable to cover the syllabus on time

Class 10 Maths Syllabus Welcome to Studit’s Class 10 Maths hub! Whether you’re studying for CBSE, ICSE, CHSE, or state board exams, our comprehensive guide to the Class 10 Maths syllabus makes learning fun, simple, and effective. Designed for students in Bhubaneswar and beyond, this index page lists all the chapters from the NCERT Class 10 Maths curriculum, complete with easy-to-understand notes, practice questions, and tips to ace your 2025-26 exams. Click the links below to explore each topic, and let Studit’s expert tutors help you excel in Maths! Class 10 Maths Chapters Chapter 1: Real Numbers 1.1 Introduction to Real Numbers: Learn the basics of real numbers and their types. 1.2 Euclid’s Division Lemma: Understand how to find HCF using this method. 1.3 The Fundamental Theorem of Arithmetic: Explore prime factorization. 1.4 Revisiting Irrational Numbers: Dive into numbers like √2 and π. 1.5 Revisiting Rational Numbers and Their Decimal Expansions: Master decimal forms. 1.6 Summary: Key takeaways and practice questions. Why Study This? Perfect for building a strong foundation in number systems for CBSE and ICSE exams. Chapter 2: Polynomials 2.1 Introduction to Polynomials: Understand polynomials and their degrees. 2.2 Geometrical Meaning of the Zeroes of a Polynomial: Visualize zeroes on graphs. 2.3 Relationship between Zeroes and Coefficients: Connect zeroes to polynomial equations. 2.4 Division Algorithm for Polynomials: Learn to divide polynomials. 2.5 Summary: Quick revision and practice problems. Why Study This? Essential for solving polynomial equations in Class 10 Maths. Chapter 3: Pair of Linear Equations in Two Variables 3.1 Introduction to Pair of Linear Equations: Explore linear equations with two variables. 3.2 Pair of Linear Equations in Two Variables: Understand their forms. 3.3 Graphical Method of Solution: Solve equations using graphs. 3.4 Algebraic Methods of Solving: Master substitution and elimination methods. 3.5 Equations Reducible to Linear Equations: Tackle complex problems. 3.6 Summary: Key concepts and practice questions. Why Study This? Crucial for solving real-life problems in CBSE and state board exams. Chapter 4: Quadratic Equations 4.1 Introduction to Quadratic Equations: Learn about quadratic polynomials. 4.2 Quadratic Equations: Understand their standard form. 4.3 Solution by Factorisation: Solve quadratics by factoring. 4.4 Solution by Completing the Square: Master this algebraic method. 4.5 Nature of Roots: Analyze roots using the discriminant. 4.6 Summary: Quick revision and practice. Why Study This? Key for algebra and board exam preparation. Chapter 5: Arithmetic Progressions 5.1 Introduction to Arithmetic Progressions: Explore sequences with a common difference. 5.2 nth Term of an AP: Find any term in the sequence. 5.3 Sum of First n Terms of an AP: Calculate sums of APs. 5.4 Summary: Key formulas and practice questions. Why Study This? Perfect for understanding patterns in Maths. Chapter 6: Triangles 6.1 Introduction to Triangles: Learn about types of triangles. 6.2 Similar Figures: Understand similarity in shapes. 6.3 Similarity of Triangles: Explore criteria for similar triangles. 6.4 Criteria for Similarity: Master AAA, SSS, and SAS rules. 6.5 Areas of Similar Triangles: Calculate areas of similar figures. 6.6 Pythagoras Theorem: Apply this theorem to right triangles. 6.7 Summary: Revision and practice problems. Why Study This? Essential for geometry in CBSE, ICSE, and CHSE syllabi. Chapter 7: Coordinate Geometry 7.1 Introduction to Coordinate Geometry: Understand the coordinate plane. 7.2 Distance Formula: Calculate distances between points. 7.3 Section Formula: Find points dividing a line segment. 7.4 Area of a Triangle: Compute areas using coordinates. 7.5 Summary: Key formulas and practice. Why Study This? A must for solving coordinate-based problems. Chapter 8: Introduction to Trigonometry 8.1 Introduction to Trigonometry: Learn about sine, cosine, and tangent. 8.2 Trigonometric Ratios: Understand ratios in right triangles. 8.3 Trigonometric Ratios of Specific Angles: Master values for 0°, 30°, 45°, 60°, 90°. 8.4 Trigonometric Ratios of Complementary Angles: Explore angle relationships. 8.5 Trigonometric Identities: Apply identities to solve problems. 8.6 Summary: Revision and practice questions. Why Study This? Key for trigonometry in board exams. Chapter 9: Some Applications of Trigonometry 9.1 Introduction to Applications of Trigonometry: Explore real-world uses. 9.2 Heights and Distances: Solve problems involving angles and heights. 9.3 Summary: Key concepts and practice. Why Study This? Perfect for applying trigonometry to practical scenarios. Chapter 10: Circles 10.1 Introduction to Circles: Learn about circles and their properties. 10.2 Tangent to a Circle: Understand tangents and their properties. 10.3 Number of Tangents from a Point: Explore tangent rules. 10.4 Summary: Revision and practice questions. Why Study This? Crucial for geometry in Class 10 Maths. Chapter 11: Constructions 11.1 Introduction to Constructions: Learn geometric constructions. 11.2 Division of a Line Segment: Divide lines using a compass. 11.3 Construction of Tangents to a Circle: Draw tangents accurately. 11.4 Summary: Key steps and practice. Why Study This? Essential for practical geometry skills. Chapter 12: Areas Related to Circles 12.1 Introduction to Areas Related to Circles: Explore circular areas. 12.2 Perimeter and Area of a Circle: Review key formulas. 12.3 Areas of Sector and Segment: Calculate parts of a circle. 12.4 Areas of Combination of Plane Figures: Solve combined shape problems. 12.5 Summary: Revision and practice questions. Why Study This? Key for mastering circular geometry. Chapter 13: Surface Areas and Volumes 13.1 Introduction to Surface Areas and Volumes: Learn about 3D shapes. 13.2 Surface Area of a Combination of Solids: Calculate combined areas. 13.3 Volume of a Combination of Solids: Find volumes of complex shapes. 13.4 Conversion of Solid from One Shape to Another: Solve conversion problems. 13.5 Frustum of a Cone: Understand frustum calculations. 13.6 Summary: Key formulas and practice. Why Study This? Essential for 3D geometry in board exams. Chapter 14: Statistics 14.1 Introduction to Statistics: Learn about data analysis. 14.2 Mean of Grouped Data: Calculate the average of data sets. 14.3 Mode of Grouped Data: Find the most frequent value. 14.4 Median of Grouped Data: Determine the middle value. 14.5 Graphical Representation: Understand cumulative frequency graphs. 14.6 Summary: Revision and practice questions. Why Study This? Crucial for data interpretation in Maths. Chapter 15: Probability 15.1 Introduction to Probability: Explore the concept of chance. 15.2 Probability – A Theoretical Approach: Learn probability calculations. 15.3 Summary:

3D Shapes Explained: A Fun Geometry Guide for Students | Studit Geometry is everywhere, from the soccer ball you kick to the juice can you drink from! At Studit, we make learning about 3D shapes fun and easy for students in Classes 1 to 12, whether you’re studying for CBSE, ICSE, CHSE, or state board exams. In this guide, we’ll explore what 3D shapes are, their types, properties, and how they appear in real life. Ready to dive into the world of solids? Let’s get started with Studit’s expert tutoring! Table of Contents What Are 3D Shapes? Types of 3D Shapes Properties of 3D Shapes Surface Area and Volume of 3D Shapes 3D Shapes and Nets Solved Examples Learn Geometry with Studit What Are 3D Shapes? 3D shapes, also called solids, are objects that have three dimensions: length, width, and height. Unlike flat 2D shapes (like a circle or square), 3D shapes have depth, making them solid objects you can hold, like a ball or a box. In geometry, 3D shapes are defined by their faces (flat or curved surfaces), edges (lines where faces meet), and vertices (points where edges meet). You see 3D shapes every day! Think of a basketball (sphere), a juice can (cylinder), or an ice cream cone (cone). Understanding 3D shapes is key for CBSE, ICSE, and state board math exams, and Studit’s tutors in Bhubaneswar are here to help you master them! Types of 3D Shapes 3D shapes can be divided into two main types: polyhedrons (with flat, straight-sided faces) and curved solids (with curved surfaces). Let’s explore the most common ones: Polyhedrons Polyhedrons are 3D shapes with flat faces and straight edges. Here are some examples: Cube: A 3D shape with 6 equal square faces, like a Rubik’s Cube or a dice. Cuboid: A 3D shape with 6 rectangular faces, like a shoebox or a book. Pyramid: A 3D shape with a polygon base (e.g., square or triangle) and triangular faces meeting at a point called the apex, like the pyramids in Egypt. Prism: A 3D shape with two identical polygon bases connected by flat faces, like a triangular prism (used in optics) or a rectangular prism (like a cereal box). Curved Solids Curved solids have at least one curved surface. Examples include: Sphere: A round 3D shape where every point on the surface is equidistant from the center, like a basketball or a globe. Cone: A 3D shape with a single circular base and one vertex, like an ice cream cone or a traffic cone. Cylinder: A 3D shape with two parallel circular bases connected by a curved surface, like a soda can or a drum. Properties of 3D Shapes Each 3D shape has unique features based on its faces, edges, and vertices. Here’s a quick overview of common 3D shapes and their properties: 3D Shape Faces Edges Vertices Cube 6 (square) 12 8 Cuboid 6 (rectangular) 12 8 Cone 2 (1 circular base, 1 curved surface) 1 1 Cylinder 3 (2 circular bases, 1 curved surface) 2 0 Sphere 1 (curved surface) 0 0 Square-based Pyramid 5 (1 square base, 4 triangular faces) 8 5 Triangular Prism 5 (2 triangular bases, 3 rectangular faces) 9 6 Need help memorizing these? Studit’s personalized tutoring makes it easy for students in Classes 4 to 12! Surface Area and Volume of 3D Shapes 3D shapes are measured by their surface area (the total area of all faces) and volume (the space they occupy). Here are the key formulas: 3D Shape Total Surface Area (TSA) Volume Cube 6a² (a = edge length) a³ Cuboid 2(lw + wh + lh) (l = length, w = width, h = height) lwh Cone πr(l + r) (r = radius, l = slant height) (1/3)πr²h Cylinder 2πr(h + r) (r = radius, h = height) πr²h Sphere 4πr² (r = radius) (4/3)πr³ These formulas are essential for solving geometry problems in CBSE, ICSE, and CHSE exams. Practice them with Studit’s expert tutors! 3D Shapes and Nets A net is a 2D shape that can be folded to form a 3D shape. Imagine cutting open a box and laying it flat—that’s its net! Here’s how nets work for common 3D shapes: Cube: A net of 6 squares arranged in a cross pattern, like unfolding a dice. Cuboid: A net of 6 rectangles, like flattening a shoebox. Cone: A net with a circular base and a curved sector, like a birthday cap cut open. Cylinder: A net with two circles (bases) and a curved rectangle, like unrolling a soda can. Square-based Pyramid: A net with a square base and four triangles, like unfolding a pyramid model. Try making nets at home to understand 3D shapes better! Studit’s tutors can guide you through hands-on activities to master this concept. Solved Examples Let’s practice with some questions: Q1: What is the surface area of a cube with an edge length of 5 cm? Solution:Surface area of a cube = 6a²= 6 × 5² = 6 × 25 = 150 cm²Answer: The surface area is 150 cm². Q2: Find the volume of a cylinder with a radius of 4 cm and height of 10 cm. (Use π = 3.14) Solution:Volume of a cylinder = πr²h= 3.14 × 4² × 10 = 3.14 × 16 × 10 = 502.4 cm³Answer: The volume is 502.4 cm³. Q3: What is the total surface area of a cone with a radius of 3 cm and slant height of 5 cm? (Use π = 3.14) Solution:Total surface area of a cone = πr(l + r)= 3.14 × 3 × (5 + 3) = 3.14 × 3 × 8 = 75.36 cm²Answer: The surface area is 75.36 cm². Need help with these problems? Studit’s tutors in Bhubaneswar offer personalized lessons to make geometry easy! Learn Geometry with Studit At Studit, we make learning 3D shapes fun and simple for students in Bhubaneswar and beyond. Whether you’re in Class 3 exploring shapes or in Class 12 preparing for board exams, our

Discovering 2D Shapes: A Fun Geometry Guide with Studit Discover the world of 2D shapes with Studit’s expert guide! Perfect for students in Classes 1 to 12 studying CBSE, ICSE, CHSE, or state board syllabi, this article makes geometry simple and fun. From circles to octagons, learn about 2D shapes, their properties, and real-life examples. Whether you’re in Bhubaneswar or learning online, Studit’s personalized tutoring can help you master math. Let’s dive into 2D shapes! Table of Contents What Are 2D Shapes? Types of 2D Shapes Properties of 2D Shapes Area and Perimeter of 2D Shapes Solved Examples Why Learn 2D Shapes with Studit? What Are 2D Shapes? 2D shapes are flat figures you can draw on paper, with only length and width. Think of a pizza, a notebook, or a traffic sign—these are all 2D shapes! In geometry, 2D shapes have unique features like sides, angles, or curves, making them a key part of math for CBSE, ICSE, and state board students. Most 2D shapes, like triangles and squares, are polygons with straight sides. Others, like circles, have curved edges. Understanding 2D shapes is essential for geometry lessons and exams, and Studit’s expert tutors in Bhubaneswar are here to make it easy! Keywords: 2D shapes, geometry for students, CBSE math, ICSE geometry Types of 2D Shapes Here are the most common 2D shapes you’ll study in school: Circle A circle is a round 2D shape where every point on the edge is equidistant from the center (radius). Examples include: A round pizza A coin A clock face Triangle A triangle is a three-sided polygon with three angles that add up to 180°. Look for triangles in: A slice of pizza A yield traffic sign A kite Square A square is a four-sided polygon with equal sides and 90° angles. It’s a regular polygon. Examples include: A chessboard A square tile A photo frame Rectangle A rectangle has four sides with opposite sides equal and parallel, all at 90° angles. Examples include: A smartphone screen A book A window Pentagon A pentagon is a five-sided polygon. In a regular pentagon, all sides and angles (108° each) are equal. Examples include: A starfish A pentagonal garden patch A home plate in baseball Octagon An octagon has eight sides and eight angles, with interior angles totaling 1080° in a regular octagon. Examples include: A stop sign An octagonal mirror A decorative plate Keywords: types of 2D shapes, polygons, regular polygons, geometry for CBSE students Properties of 2D Shapes Each 2D shape has unique properties that define it. Here’s a quick overview: 2D Shape Sides Angles Symmetry Circle None (curved) 360° total Infinite Triangle 3 180° total Up to 3 (equilateral) Square 4 equal 4 right (90°) 4 lines Rectangle 2 pairs equal 4 right (90°) 2 lines Pentagon 5 5 (108° in regular) Up to 5 Octagon 8 8 (135° in regular) Up to 8 These properties are key for solving geometry problems. Studit’s personalized tutoring can help you master them, whether you’re in Class 4 or Class 10! Keywords: properties of 2D shapes, geometry basics, math tutoring Bhubaneswar Area and Perimeter of 2D Shapes The area is the space inside a 2D shape, and the perimeter is the distance around its edges. Here are the formulas for common 2D shapes: 2D Shape Area Perimeter Circle πr² (r = radius) 2πr Triangle ½ × base × height Sum of all sides Square side² 4 × side Rectangle length × breadth 2(length + breadth) Pentagon (regular) (5/4) × side² × cot(π/5) 5 × side Octagon (regular) 2 × side² × (1 + √2) 8 × side These formulas are essential for CBSE, ICSE, and state board exams. Practice with Studit’s expert tutors to ace your geometry questions! Keywords: area of 2D shapes, perimeter of polygons, CBSE geometry formulas Solved Examples Try these practice questions to test your skills: Q1: What is the area of a square with a side length of 7 cm? Solution: Area of a square = side² = 7 × 7 = 49 cm² Answer: 49 cm² Q2: Find the perimeter of a rectangle with a length of 12 cm and a breadth of 5 cm. Solution: Perimeter of a rectangle = 2(length + breadth) = 2(12 + 5) = 2 × 17 = 34 cm Answer: 34 cm Q3: What is the area of a circle with a radius of 3 cm? (Use π = 3.14) Solution: Area of a circle = πr² = 3.14 × 3² = 3.14 × 9 = 28.26 cm² Answer: 28.26 cm² Need help? Studit’s tutors in Bhubaneswar offer personalized home tuition and online classes to make geometry easy! Keywords: geometry practice questions, math for CBSE students, Studit tutoring Why Learn 2D Shapes with Studit? At Studit, we make geometry fun and accessible for students in Bhubaneswar and beyond. Whether you’re learning shapes in Class 2 or preparing for Class 12 board exams, our expert tutors and innovative Studit app help you excel. Here’s why: Personalized Tutoring: One-on-one home tuition tailored to your learning style. Free Demo Classes: Try our teaching before committing. Studit App: Book classes, track progress, and get feedback anytime. 24/7 Support: We’re here to answer your questions, day or night. Ready to master 2D shapes? Visit www.studit.in or download the Studit app to book a free demo class today. Shape your math success with Studit! Keywords: math tutoring Bhubaneswar, personalized geometry lessons, Studit app Frequently Asked Questions (FAQs) Q1: What are 2D shapes? 2D shapes are flat figures with length and width, like circles, triangles, and squares. Q2: What are common 2D shapes? Circles, triangles, squares, rectangles, pentagons, and octagons are common 2D shapes. Q3: What is a regular polygon? A regular polygon has equal sides and angles, like a square or regular pentagon. Q4: How do I calculate the area of a triangle? Use the formula: Area = ½ × base × height. Q5: What are real-life examples of 2D shapes? A pizza (circle), a traffic sign (triangle),

Understanding the 180-Degree Angle: A Straight Path to Geometry Success with Studit At Studit, we believe learning geometry should be fun and straightforward, just like a 180-degree angle! Whether you’re a Class 6 student exploring angles for the first time or a Class 10 student preparing for board exams, understanding the 180-degree angle is a key step in mastering geometry. Let’s dive into what a 180-degree angle is, how to measure and draw it, and why it matters for your studies! What is a 180-Degree Angle? A 180-degree angle is called a straight angle because it forms a perfect straight line. Imagine stretching your arms out wide to make a straight line—that’s what a 180-degree angle looks like! In geometry, angles are classified based on their size, and here’s a quick guide to help you remember: Acute Angle: Less than 90° (think sharp and small, like a slice of pizza!) Right Angle: Exactly 90° (like the corner of your notebook) Obtuse Angle: More than 90° but less than 180° (a bit wider than a right angle) Straight Angle: Exactly 180° (a straight line, like a ruler) Reflex Angle: More than 180° but less than 360° Full Rotation: Exactly 360° (a complete circle, like spinning around!) The 180-degree angle is special because it’s the angle you see when two lines form a straight path, like a road stretching out in front of you. Why is the 180-Degree Angle Important? Understanding the 180-degree angle is key for solving geometry problems, especially in topics like triangles and supplementary angles. For example, did you know that the sum of all interior angles in a triangle always equals 180 degrees? Or that two angles that add up to 180 degrees are called supplementary angles? These concepts are crucial for CBSE, ICSE, and state board exams, and Studit’s expert tutors are here to help you master them! How to Measure a 180-Degree Angle Using a Protractor Measuring a 180-degree angle is easy with a protractor. Follow these steps, and you’ll be a pro in no time: Draw a Straight Line: Use a ruler to draw a straight line on your paper. Label one end as point A and the other as point B. Mark the Vertex: Place a dot anywhere on the line (let’s call it point O). This is the vertex of your angle. Align the Protractor: Place the center of the protractor on point O, making sure the baseline of the protractor lines up with the line (A to B). Find 180°: Look at the protractor’s scale. The 180° mark should align perfectly with the straight line, confirming it’s a straight angle! With Studit’s personalized tutoring, our teachers can guide you step-by-step, whether you’re practicing in-person or through our app. How to Draw a 180-Degree Angle Using a Compass Don’t have a protractor? No problem! You can draw a 180-degree angle using a compass. Here’s how: Draw a Line: Use a ruler to draw a straight line and label it XY. Mark a Point: Choose a point on the line (call it O). Draw an Arc: With point O as the center, use a compass to draw an arc that crosses the line on both sides (label these points P and Q). Check Your Angle: The angle formed by points P, O, and Q is 180 degrees because it lies on a straight line. Want to practice this with a tutor? Book a free demo class with Studit, and we’ll help you perfect your compass skills! Fun Facts About the 180-Degree Angle It’s Everywhere!: Look around—you’ll see 180-degree angles in straight roads, the edge of a table, or even when you stretch a rubber band tight. Supplementary Angles: If one angle is 70°, its supplementary angle (which adds up to 180°) is 110°. Try this with any angle pair! Triangles and 180°: The sum of angles in any triangle is always 180°. This is a must-know for geometry exams! Try These Practice Questions Q.1: If a right angle is divided into two parts and one part measures 30°, find the other angle. Solution:Let the unknown angle be xRight angle = 90°Given one angle = 30° So,x + 30 = 90x = 90 – 30 = 60° Answer: The other angle is 60° Q.2: Two angles form a linear pair. One of them is 110°. Find the other. Solution:Linear pair angles are supplementary (sum = 180°)Let the other angle be x x + 110 = 180x = 180 – 110 = 70° Answer: The other angle is 70° Q.3: If two complementary angles are equal, find the value of each. Solution:Complementary angles add up to 90°Let each angle be x x + x = 902x = 90x = 90 ÷ 2 = 45° Answer: Both angles are 45° Q.4: One angle is 3 times its complement. Find both angles. Solution:Let the complement be x, so the other angle is 3xx + 3x = 904x = 90x = 22.5°, 3x = 67.5° Answer: The angles are 22.5° and 67.5° Need help solving these? Studit’s tutors can explain these problems in a way that makes sense to you, whether you’re in Class 5 or Class 12. Learn Geometry with Studit! At Studit, we make geometry exciting and easy to understand. Our expert tutors in Bhubaneswar provide personalized home tuition and online classes to help you master angles, triangles, and more. With the Studit app, you can track your progress, book sessions, and even try a free demo class to see how we can help you shine in math! Ready to conquer geometry? Visit www.studit.in or download the Studit app to get started today. Let’s make learning as straight as a 180-degree angle!