Explore Exams
Login Signup
Sign in Open App
CBSE Class 7  >  Class 7 Notes  >  Mathematics Olympiad   >  Chapter Notes - Perimeter and Area

Perimeter and Area Class 7 Notes Maths Chapter 9

What is Perimeter and Area?

Area and perimeter are two fundamental concepts in plane geometry that describe the size and shape of a 2D object.

Perimeter

  • The perimeter of a shape is the total length of its boundary.
  • It is calculated by adding the lengths of all the sides of the shape.
  • Perimeter is measured in linear units such as metres (m), centimetres (cm) or inches (in).
Perimeter

Area

  • The area of a shape is the amount of surface enclosed within its boundary.
  • Area is measured in square units such as square metres (m2), square centimetres (cm2) or square inches (in2).
Area

Area of Parallelograms

A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.

Area of Parallelograms

To find the area of a parallelogram,you can follow these steps:

  1. Choose a base (any one side of the parallelogram).
  2. Determine the height (the perpendicular distance from the chosen base to the opposite side).
  3. Use the formula: Area = Base × Height.
Area of Parallelograms

MULTIPLE CHOICE QUESTION

Try yourself: What is the formula to calculate the area of a parallelogram?

A

Area = Base x Height

B

Area = Length x Width

C

Area = Base x Perimeter

D

Area = Height x Width

Let us understand this with an example:

Example 1: Find the area of the following parallelograms:

Area of Parallelograms

Ans:

Base = 8 cm

Height = 3.5 cm

Area of parallelogram = Base × Height

Area of parallelogram = 8 cm × 3.5 cm

= 28 cm2

Area of Parallelograms

Ans:

Base = 8 cm

Height = 2.5 cm

Area of parallelogram = Base × Height

Area of parallelogram = 8 cm × 2.5 cm

= 20 cm2

Example 2: PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm, find:

(a) the area of the parallelogram PQRS

(b) QN, if PS = 8 cm

Area of Parallelograms

Ans:

Given: SR = 12 cm, QM = 7.6 cm, PS = 8 cm

(a). Area of parallelogram = base × height

Area = 12 × 7.6

= 91.2 cm2

(b). Since area = PS × QN, we have 91.2 = 8 × QN

QN = 91.2 ÷ 8

= 11.4 cm

MULTIPLE CHOICE QUESTION

Try yourself: The area of the parallelogram ABCD in which AB = 6.2 cm and the perpendicular from C on AB is 5 cm is

A

30 cm2

B

29 cm2

C

28 cm2

D

31 cm2

Area of Triangle

A triangle is a polygon with three vertices and three sides. A triangle with vertices A, B and C is denoted by ABC.

Triangle ABCTriangle ABC

To find the area of a triangle within a parallelogram, you can follow these steps:

1. Identify the triangle

  • Choose the triangle whose area is required.
  • The base of the triangle is one side of the parallelogram.
  • The height is the perpendicular distance from the base to the opposite vertex or side.

2. Understand the relationship

  • A parallelogram can be divided into two congruent triangles by a diagonal.
  • Therefore, the area of the parallelogram is twice the area of one of these triangles.

3. Calculate the area of the parallelogram

  • Use the formula Area (parallelogram) = Base × Height.
3. Calculate the area of the parallelogram

4. Apply the relationship for the triangle

  • Area of each triangle = 1/2 × (Area of parallelogram)
Parallelogram ABCDParallelogram ABCD

Thus, Area of a triangle = 1/2 × base × height.

All congruent triangles are equal in area, but triangles equal in area need not be congruent.

Example 1: Find BC, if the area of triangle ABC is 36 cm2 and the height AD is 3 cm.

4. Apply the relationship for the triangle

Ans:

Area of triangle ABC = 1/2 × base × height

36 = 1/2 × BC × 3

36 = (3/2) × BC

BC = 36 × (2/3)

= 24 cm

MULTIPLE CHOICE QUESTION

Try yourself: Find the area of ∆ ABC
4. Apply the relationship for the triangle

A

3 cm2

B

4 cm2

C

6 cm2

D

12 cm2

Example 2: Triangle ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of triangle ABC. What will be the height from C to AB, i.e., CE?

4. Apply the relationship for the triangle

Ans:

Area of triangle ABC = 1/2 × base × height

Here base = BC = 9 cm and height AD = 6 cm

Area = 1/2 × 9 × 6

= 27 cm2

To find CE (height from C to AB), use area formula with base AB = 7.5 cm:

Area = 1/2 × AB × CE

27 = 1/2 × 7.5 × CE

27 = 3.75 × CE

CE = 27 ÷ 3.75

= 7.2 cm

Circles

A circle is the set of all points in a plane that are at a fixed distance from a fixed point called the centre.

CircleCircle
  • Diameter: A line segment that passes through the centre of a circle and whose endpoints lie on the circle.
  • Radius: A line segment joining the centre of the circle to any point on the circle.

Circumference of Circle

The distance around a circular region is called its circumference.

Circumference of Circle
Circumference of Circle

where,

  • r is the radius of the circle
  • π is an irrational number, whose value is approximately equal to 3.14 or it can be taken as 22/7
  • Diameter(d) of a circle is equal to twice the radius(r) =2r 
  • Circumference = 2πr = πd.

Note: Circles having the same centre but different radii are called concentric circles.

Circumference of Circle

MULTIPLE CHOICE QUESTION

Try yourself: What is the formula for the circumference of a circle?

A

Circumference = 2πr

B

Circumference = πr2

C

Circumference = d/2

D

Circumference = πr/2

Example: If the radius of the circle is 25 units, find the circumference of the circle. (Take π = 3.14)

Ans:

Given radius r = 25 units

Circumference formula: C = 2πr

C = 2 × 3.14 × 25

= 157 units

Therefore, the circumference is 157 units.

Area of Circle

The area of a circle is the region enclosed by its circumference.

Area of Circle

where 

  • r is the radius of the circle
  • A is the area of the circle 
  • π is an irrational number, whose value is approximately equal to 3.14 or it can be taken as 22/7

Example 1: The radius of a circular pipe is 10 cm. What length of tape is required to wrap once around the pipe? (π = 3.14)

Ans:

Radius r = 10 cm

Length of tape required = circumference of pipe = 2πr

= 2 × 3.14 × 10

= 62.8 cm

Therefore, the tape length needed is 62.8 cm.

Example 2: Find the perimeter of the given shape. (Take π = 22/7)

Area of Circle

Ans:

In the figure, each side of the square has a semicircle whose diameter equals the side of the square.

Circumference of a full circle with diameter d = πd

Circumference of a semicircle = 1/2 × πd

Given d = 14 cm, semicircle circumference = 1/2 × 22/7 × 14= 22 cm

There are four semicircles; total perimeter contributed by semicircles = 4 × 22 cm = 88 cm

Therefore, the perimeter of the given figure is 88 cm.

Example 3: Diameter of a circular garden is 9.8 m. Find its area.

Ans:

Diameter d = 9.8 m

Radius r = d ÷ 2 = 9.8 ÷ 2= 4.9 m

Area = πr2

Using π = 22/7, Area = 22/7 × 4.9 × 4.9= 75.46 m2

Example 4: The adjoining figure shows two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm. Find:

(a) the area of the larger circle
(b) the area of the smaller circle
(c) the shaded area between the two circles. (π = 3.14)

Area of Circle

Ans:

(a) Radius of the larger circle = 10 cm So, area of the larger circle = πr2 = 3.14 × 10 × 10 = 314 cm2
(b) Radius of the smaller circle = 4 cm Area of the smaller circle = πr2 = 3.14 × 4 × 4 = 50.24 cm2
(c) Area of the shaded region = (314 - 50.24) cm2 = 263.76 cm2

MULTIPLE CHOICE QUESTION

Try yourself: The area of a circle is 2464m2 , then the diameter is

A

56 m

B

154 m

C

176 m

D

none of these

The document Chapter Notes - Perimeter and Area is a part of the Class 7 Course Mathematics Olympiad Class 7.
All you need of Class 7 at this link: Class 7
Join Course for Free

FAQs on Chapter Notes - Perimeter and Area

1. How do I calculate the perimeter of different shapes like squares, rectangles, and triangles?
Ans. Perimeter is the total distance around a closed shape. For a square, multiply one side by 4. For a rectangle, add all four sides or use 2(length + breadth). For a triangle, add all three sides together. Each formula depends on the shape's dimensions, making perimeter calculation straightforward once you identify which shape you're measuring.
2. What's the difference between perimeter and area, and why do I need to know both?
Ans. Perimeter measures the outer boundary or distance around a shape, while area measures the space inside it. Perimeter uses linear units (cm, m), whereas area uses square units (cm², m²). Understanding both is essential in CBSE Class 7 geometry because they solve different real-world problems-perimeter for fencing, area for carpeting or painting surfaces.
3. How do I find the area of a circle, and what does the radius have to do with it?
Ans. The area of a circle is calculated using the formula A = πr², where r is the radius. The radius is the distance from the circle's centre to its edge, and squaring it accounts for the two-dimensional space. Using π (approximately 3.14 or 22/7), this formula determines exactly how much surface the circular region covers.
4. Why do some rectangles with the same perimeter have different areas?
Ans. Rectangles with identical perimeters can have different dimensions, resulting in different areas. For example, a 6×4 rectangle and a 7×3 rectangle both have perimeter 20, but areas of 24 and 21 square units respectively. This happens because area depends on both length and breadth multiplied together, not just their sum-a key concept in understanding how perimeter and area relate differently to shape dimensions.
5. What are the formulas for calculating the area of triangles and trapezoids in Class 7 geometry?
Ans. Triangle area is calculated as A = (1/2) × base × height, where height is perpendicular to the base. Trapezoid area uses A = (1/2) × (sum of parallel sides) × height. Both formulas require identifying the correct base and perpendicular height measurement. Refer to mind maps and flashcards on EduRev to visualise these shapes and practise applying formulas accurately for your exams.
About this Document
20.5K Views
4.88/5 Rating
May 19, 2026 Last updated
Related Exams
Document Description: Chapter Notes - Perimeter and Area for Class 7 2026 is part of Mathematics Olympiad Class 7 preparation. The notes and questions for Chapter Notes - Perimeter and Area have been prepared according to the Class 7 exam syllabus. Information about Chapter Notes - Perimeter and Area covers topics like and Chapter Notes - Perimeter and Area Example, for Class 7 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Chapter Notes - Perimeter and Area.
Introduction of Chapter Notes - Perimeter and Area in English is available as part of our Mathematics Olympiad Class 7 for Class 7 & Chapter Notes - Perimeter and Area in Hindi for Mathematics Olympiad Class 7 course. Download more important topics related with notes, lectures and mock test series for Class 7 Exam by signing up for free. Class 7: Chapter Notes - Perimeter and Area
Description
Chapter Notes of Mathematics Olympiad Class 7 with clear explanations of key concepts & important topics of the chapter, to help you underst& lessons better & revise quickly, & crack the Class 7 exam.
Information about Chapter Notes - Perimeter and Area
In this doc you can find the meaning of Chapter Notes - Perimeter and Area defined & explained in the simplest way possible. Besides explaining types of Chapter Notes - Perimeter and Area theory, EduRev gives you an ample number of questions to practice Chapter Notes - Perimeter and Area tests, examples and also practice Class 7 tests
Explore Courses for Class 7 exam
Get EduRev Notes directly in your Google search
Related Searches
Chapter Notes - Perimeter and Area, practice quizzes, past year papers, Viva Questions, Extra Questions, MCQs, Important questions, Previous Year Questions with Solutions, Summary, Semester Notes, study material, pdf , mock tests for examination, Free, Objective type Questions, Sample Paper, Chapter Notes - Perimeter and Area, Exam, shortcuts and tricks, video lectures, ppt, Chapter Notes - Perimeter and Area;
Additional Information about Chapter Notes - Perimeter and Area for Class 7 Preparation

Chapter Notes - Perimeter and Area Free PDF Download

The Chapter Notes - Perimeter and Area is an invaluable resource that delves deep into the core of the Class 7 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Chapter Notes - Perimeter and Area now and kickstart your journey towards success in the Class 7 exam.

Importance of Chapter Notes - Perimeter and Area

The importance of Chapter Notes - Perimeter and Area cannot be overstated, especially for Class 7 aspirants. This document holds the key to success in the Class 7 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Chapter Notes - Perimeter and Area

Chapter Notes - Perimeter and Area Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Chapter Notes - Perimeter and Area. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Chapter Notes - Perimeter and Area Notes on EduRev are your ultimate resource for success.

Chapter Notes - Perimeter and Area Class 7 Questions

The "Chapter Notes - Perimeter and Area Class 7 Questions" guide is a valuable resource for all aspiring students preparing for the Class 7 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Chapter Notes - Perimeter and Area on the App

Students of Class 7 can study Chapter Notes - Perimeter and Area alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Chapter Notes - Perimeter and Area, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Chapter Notes - Perimeter and Area is prepared as per the latest Class 7 syllabus.
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup