Question

In this figure, AOB is a quarter circle of radius 10 and PQRO is a rectangle of perimeter 26. The perimeter of the shaded region is -

• A. 13 + 5$\pi$
• B. 17 + 5$\pi$
• C. 7 + 10$\pi$
• D. 7 + 5$\pi$

Answer 1

The correct option is D 7 + 5$\pi$

According to figure, $r^2=l^2+b^2$

Given $r=10(l+b)=13$

Perimeter of shaded region

$=\frac{2\pi \left(r\right)}{4}+r-l+r-b=\frac{\pi \left(10\right)}{2}+2r-(l+b)=5\pi +20-13=5\pi +7$