NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.3

Question 8

Step 1: Observe the figure.

The field has three parts:

• A rectangle in the middle (length = 8 m, height = 4 m).
• A semicircle on the left side with radius 3 m (because height = 6 m ⇒ diameter = 6 m ⇒ radius = 3 m).
• A semicircle on the right side with radius 2 m (because height = 4 m ⇒ diameter = 4 m ⇒ radius = 2 m).

Step 2: Find the area of the rectangle.

Area of rectangle = length × breadth

= 8 m × 4 m = 32 m².

Step 3: Find the area of the right semicircle.

Formula for area of a semicircle = (1/2) × π × r²

Here radius r = 2 m.

So, area = (1/2) × π × (2 m)²

= (1/2) × π × 4 m²

= 2π m².

Step 4: Find the area of the left semicircle.

Radius r = 3 m (since diameter = 6 m).

Area = (1/2) × π × (3 m)²

= (1/2) × π × 9 m²

= 4.5π m².

Step 5: Add all areas.

Total area = Rectangle + Right semicircle + Left semicircle

= 32 m² + 2π m² + 4.5π m²

= 32 m² + 6.5π m².

Step 6: Approximate value using π = 3.1416.

= 32 + 6.5 × 3.1416

= 32 + 20.42

= 52.42 m² (approx).

Final Answer: The area of the shaded field is \(32 + 6.5\pi\;\text{m}^2\) ≈ 52.42 m².