Question

If AB = 10 cm, what is the area of the shaded portion? It is given that OPA and OQB are quadrants of a circle and AB is a tangent to them. AMR and RNB are two identical semicircles.

• A. $25(2-\frac{\pi }{4})$
• B. $25\frac{\pi }{4}$
• C. $50-\frac{25\pi }{2}$
• D. None of these

Answer 1

The correct option is A

$25(2-\frac{\pi }{4})$

Area of two small semicircles
$=2\times \frac{\pi {\left(\frac{5}{2}\right)}^2}{2}=25\frac{\pi }{4}c{m}^2$



Area of the shaded region=Area of the rectangle
- (Area of the quandrants APQ and BQO)
$=(5\times 10)-2\pi 5^2\times \frac{1}{4}=50-25\frac{\pi }{2}$
$\therefore$ Total area of the shaded region
$=50-\frac{25\pi }{2}+\frac{25\pi }{4}=25(2-\frac{\pi }{4})$