Question

In the fig, find the perimeter of the shaded region, if $ABCD$ is a square of side $21cm$ and $APB$ and $CPD$ are semicircles.

Answer 1

Given: ABCD is square of side $21cm.$

$AB=BC=CD=DA=21cm$

$APB$ and $CPD$ are two semicircle.

Diameter of above semicircle $=CD=AB=21cm$

$\therefore$ radius, r $=\frac{21}{2}cm$

The perimeter of the above semicircles $=$ Length of the $CPD$ or Length of $APB=\frac{2\pi \times r}{2}=\pi \times r$

Perimeter of the shaded region $=AB+BC+2\times$perimeter of semicircle

$=21+21+2\times \frac{(\pi \times 21)}{2}$

$=42+\frac{22}{7}\times 21$

$=42+22\times 3$

$=108cm$

So, the perimeter of the shaded region is $108cm$.