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 B $17+5\pi$

Since $AOB$ is the quarter circle the radius of $AOB$ circle has length $\left(\frac{2\pi \left(10\right)}{4}\right)=5\pi$
Given $QO=10$
$QO=RP=10$
Since $QO$ is the radius $RP$ also equals
Perimeter $=26$
$\frac{26}{2}=13=PO+RO$
$10+10=20$
$20-13=7$
$BR+AP=7$
$5\pi +10+7=5\pi +17$