Question

In the figure, ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of ${180}^{\circ }$ have been cut-off. Calculate the length of the boundary of the shaded region.

Answer 1

Given $AB=20$ cm and $BC=14$ cm

$\Rightarrow$ Here, two semicircle present in rectangle with diameter $14cm$.

$\Rightarrow$ Radius of semicircle $\left(r\right)=\frac{14}{2}=7cm$

Length of ARC$=r\times \theta$ here $\theta =\pi$

Length of the boundary$=AB+DC+2\times \text{length of ARC's}$

$=AB+DC+2\times \pi r$

$=20+20+2\times \frac{22}{7}\times 7$

$=40+44=84cm$