Class 7 Notes - Perimeter and Area

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Perimeter and Area

In this chapter, students will learn how to calculate the perimeter and area of various two-dimensional shapes, understand their real-life applications, and solve related word problems.

1. What is Perimeter?

The perimeter is the total length of the boundary of a closed figure. It is measured in units such as centimeters (cm), meters (m), etc.

  • Perimeter of a Rectangle: 2 × (Length + Breadth)
  • Perimeter of a Square: 4 × Side
  • Perimeter of a Triangle: Sum of all sides
  • Perimeter of a Regular Polygon: Number of sides × Length of one side

2. What is Area?

The area is the amount of surface enclosed by a closed figure. It is measured in square units such as cm², m², etc.

  • Area of a Rectangle: Length × Breadth
  • Area of a Square: Side × Side
  • Area of a Triangle: (Base × Height) ÷ 2
  • Area of a Parallelogram: Base × Height

3. Real-life Applications

  • Fencing a garden (perimeter)
  • Laying tiles on a floor (area)
  • Framing a picture (perimeter)
  • Painting a wall (area)

4. Examples

Example 1: Find the perimeter of a rectangle with length 8 cm and breadth 5 cm.
Solution: Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm
Example 2: Find the area of a square with side 6 m.
Solution: Area = 6 × 6 = 36 m²
Example 3: A triangle has base 10 cm and height 4 cm. Find its area.
Solution: Area = (10 × 4) ÷ 2 = 40 ÷ 2 = 20 cm²

5. Word Problems

  1. A rectangular park is 50 m long and 30 m wide. What is its perimeter and area?
  2. A square field has a side of 15 m. Find its perimeter and area.
  3. The sides of a triangle are 7 cm, 8 cm, and 9 cm. What is its perimeter?
  4. A parallelogram has a base of 12 cm and height of 5 cm. Find its area.

6. Practice Exercises

  1. Find the perimeter of a square whose side is 9 cm.
  2. Calculate the area of a rectangle with length 14 m and breadth 6 m.
  3. A triangle has sides 5 cm, 6 cm, and 7 cm. What is its perimeter?
  4. Find the area of a square with side 11 m.

7. Common Mistakes

  • Confusing perimeter with area.
  • Forgetting to use square units for area.
  • Adding sides instead of multiplying for area.
  • Using wrong formulas for different shapes.

8. Summary

  • Perimeter is the total length around a figure.
  • Area is the surface covered by a figure.
  • Use correct formulas for each shape.
  • Always write units (cm, m, cm², m²) in your answers.