Question

In given figure, ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded region.

Answer 1

Given $AB=14cm,BC=AD=7cm$

we know that the area of rectangle$=l\times b$

area of the semicircle$=\frac{\pi \times r^2}{2}$

Here the radius of the big semicircle$\left(r_1\right)=\frac{14}{2}=7cm$

the radius of the small semicircle$\left(r_2\right)=\frac{7}{2}cm$

Area of shaded region = Area ABCD + 2 $\times$ area small semi-circle - area big semi-circle

$=(l\times b)+2\cdot \frac{1}{2}\pi {r_1}^2-\frac{1}{2}\pi {r_2}^2$

$=(14\times 7)+2\times \frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}-\frac{1}{2}\times \frac{22}{7}\times 7\times 7$

$=98+38.5-77=59.5{cm}^2$