#### Question

In the figure given below, ABCD is the 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 = 22/7`).

#### Solution

Considering the given figure:

Given dimensions of the rectangle: AB = 14 cm and BC = 7 cm

⇒ Radius of the quarter circle = 7 cm

Area of the quarter circle = `1/2 xx 22/7 xx 7^2` sq. cm `= 77/2` sq. cm

Since EC = 7 cm and DC = 14 cm, we have

Therefore, radius of the semi circle = `7/2` cm

=> Area of the semi circle = `1/2 xx 22/7 xx (7/2)^2 sq. cm = 77/4 sq. cm`

Now, are of rectangle ABCD = AB x BC = 14 x 7 = 98 sq. cm

∴ Required area = Area of rectangle ABCD - [Area(BCEF) + Area(DGE)]

`= 98 - 77/2 - 77/4`

`= 161/4`

= 40.25 sq. cm