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Mathematics Class 7 - Perimeter And-Area Notes

Comprehensive study notes for Class 7 - Perimeter And-Area olympiad preparation

Perimeter and Area

Welcome to the chapter on Perimeter and Area for Class 7. In this chapter, you will learn how to find the perimeter and area of different shapes, understand their formulas, and solve real-life problems. By the end of this chapter, you will be able to calculate perimeter and area for rectangles, squares, triangles, circles, and more!

Introduction

Perimeter is the distance around a shape. Area is the space inside a shape. Both are important in mathematics and in daily life, like fencing a garden or laying tiles on a floor.

Perimeter

The perimeter of a shape is the total length of its boundary.

  • Rectangle: Perimeter = 2 Ă— (Length + Breadth)
  • Square: Perimeter = 4 Ă— Side
  • Triangle: Perimeter = Sum of all sides
  • Circle: Perimeter (Circumference) = 2 Ă— Ď€ Ă— Radius

Example: The perimeter of a rectangle with length 8 cm and breadth 5 cm is 2 Ă— (8 + 5) = 26 cm.

Area

Area is the amount of surface covered by a shape.

  • Rectangle: Area = Length Ă— Breadth
  • Square: Area = Side Ă— Side
  • Triangle: Area = ½ Ă— Base Ă— Height
  • Circle: Area = Ď€ Ă— Radius Ă— Radius

Example: The area of a square with side 6 cm is 6 × 6 = 36 cm².

Units of Perimeter and Area

  • Perimeter is measured in units like cm, m, km.
  • Area is measured in square units like cm², m², km².

Word Problems

Use perimeter and area formulas to solve real-life problems. Read the question, choose the correct formula, and solve.

  • Example: If a garden is 10 m long and 8 m wide, what is its area? (10 Ă— 8 = 80 m²)
  • Example: What is the perimeter of a triangle with sides 5 cm, 7 cm, and 9 cm? (5 + 7 + 9 = 21 cm)

Fun Activity: Measure and Calculate!

Use a ruler to measure the sides of your notebook. Find its perimeter and area!

Summary

  • Perimeter is the distance around a shape.
  • Area is the space inside a shape.
  • Use formulas to calculate perimeter and area for different shapes.

Practice Questions

  1. Find the perimeter of a rectangle with length 12 cm and breadth 7 cm.
  2. Find the area of a square with side 9 cm.
  3. Find the area of a triangle with base 10 cm and height 5 cm.
  4. Find the circumference of a circle with radius 4 cm (use π = 3.14).
  5. A rectangular field is 20 m long and 15 m wide. What is its perimeter and area?

Challenge Yourself

  • Draw a shape and calculate its perimeter and area.
  • Make a word problem using area or perimeter and solve it.

Did You Know?

  • The Great Wall of China is the longest wall in the world—imagine its perimeter!
  • Area helps us know how much paint or tiles we need for a surface.

Glossary

  • Perimeter: The total length around a shape.
  • Area: The space inside a shape.
  • Formula: A rule or equation used to calculate something.
  • Unit: Standard measurement (cm, m, cm², m²).

Answers to Practice Questions

  1. 38 cm
  2. 81 cm²
  3. 25 cm²
  4. 25.12 cm
  5. Perimeter: 70 m, Area: 300 m²

Practice perimeter and area to solve real-life problems and become a geometry expert!

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