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
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
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
Solution: Area = (10 × 4) ÷ 2 = 40 ÷ 2 = 20 cm²
5. Word Problems
- A rectangular park is 50 m long and 30 m wide. What is its perimeter and area?
- A square field has a side of 15 m. Find its perimeter and area.
- The sides of a triangle are 7 cm, 8 cm, and 9 cm. What is its perimeter?
- A parallelogram has a base of 12 cm and height of 5 cm. Find its area.
6. Practice Exercises
- Find the perimeter of a square whose side is 9 cm.
- Calculate the area of a rectangle with length 14 m and breadth 6 m.
- A triangle has sides 5 cm, 6 cm, and 7 cm. What is its perimeter?
- 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.