Question

In the figure given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed.

Calculate the area of the remaining piece of the rectangle. (Take $\pi$ $=\frac{22}{7}$)

Answer 1

Area of rectangle = $14\times 7=98$ $c{m}^2$

Radius of semicircle = $\frac{7}{2}$ cm

Area of semicircle = $\frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{4}=19.25$ $c{m}^2$

Radius of quarter circle $=7$ cm

Area of quarter circle = $\frac{1}{4}\times \frac{22}{7}\times 7\times 7=38.5$ $c{m}^2$

Therefore,

Required area = $98-19.25-38.5=40.25$ $c{m}^2$