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

Question 13

Step 1: Each shaded region is a sector of a circle. The radius of each sector is given as \(r = 14\,\text{cm}\).

Step 2: The angle of each sector is the interior angle of the triangle at that vertex.

Step 3: The sum of the three interior angles of any triangle is always \(180^\circ\).

Step 4: So, if we add the shaded regions at all three vertices, it is the same as one sector of radius 14 cm with angle \(180^\circ\).

Step 5: Formula for the area of a sector is:

\(\text{Area of sector} = \dfrac{\theta}{360^\circ} \times \pi r^2\)

Step 6: Here \(\theta = 180^\circ\) and \(r = 14\,\text{cm}\).

\(\text{Area} = \dfrac{180}{360} \times \pi \times 14^2\)

Step 7: Simplify:

\(= \dfrac{1}{2} \times \pi \times 196\)

\(= 98\pi\,\text{cm}^2\)

Step 8: Approximate using \(\pi \approx 3.1416\):

\(98 \times 3.1416 \approx 307.88\,\text{cm}^2\)

Final Answer: The total shaded area is \(98\pi\,\text{cm}^2 \approx 307.88\,\text{cm}^2\).