Question

In this figure, $AOB$ is a quarter circle of radius $10cm$ and $PQRO$ is a rectangle of perimeter $26cm$. 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 $17+5\pi$

$RP=OQ=r=10$
Perimeter of $OPQR=26$
$2(\ell +b)=26$
$\ell +b=13$
Perimeter of shaded portion
$=PA+\widehat{AQB}+BR+RP$
$=r-\ell +\frac{2\pi r}{4}+r-b+r$
$=3r-(\ell +b)+\frac{\pi r}{2}$
$=3\times 10-13+\frac{\pi \times 10}{2}$
$=30-13+5\pi =17+5\pi$