NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.4

Question 6

Step 1: Formula for trapezium area

The area of a trapezium is given by:

\( \text{Area} = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height} \)

Step 2: Substitute values

Here, \(AB = 18\,\text{cm}\), \(DC = 32\,\text{cm}\), and height = \(14\,\text{cm}\).

So, \( \text{Area} = \dfrac{1}{2} (18 + 32) \times 14 \)

= \( \dfrac{1}{2} (50) \times 14 \)

= \( 25 \times 14 = 350\,\text{cm}^2 \).

Step 3: Find area of circular parts

At each corner A, B, C, D, a quarter-circle is drawn with radius \(7\,\text{cm}\).

Four quarter-circles together make one complete circle.

Area of a circle = \( \pi r^2 \).

Here, \(r = 7\,\text{cm}\).

So, area of the full circle = \( \pi \times 7^2 = 49\pi\,\text{cm}^2 \).

Step 4: Subtract to get shaded area

Shaded region = area of trapezium – area of circle

= \(350 - 49\pi\,\text{cm}^2 \).

Step 5: Approximate value

Take \(\pi \approx 3.14\).

So, \(49\pi \approx 49 \times 3.14 = 153.9\,\text{cm}^2 \).

Therefore, shaded region = \(350 - 153.9 = 196.1\,\text{cm}^2 \).