Question

In the given figure, ABCD is a rectangle with AB = 14 cm, BC = 7 cm. If a quarter circle BCEF and semicircle DEG are removed, calculate the area of the remaining part of the rectangle (shaded region). `["Take"  π = 22/7]`

Answer 1

Given:

• Rectangle ABCD with AB = 14 cm, BC = 7 cm.
• A quarter circle BCEF with radius BC = 7 cm is removed.
• A semicircle DEG with diameter DE = `"AB"/2 = 14/2` = 7 cm is removed.
• `π = 22/7`.

Stepwise Calculation:

1. Area of rectangle ABCD:

Area = AB × BC

= 14 × 7

= 98 cm²

2. Area of the quarter circle BCEF:

Radius = BC = 7 cm.

Area of full circle = πr²

= `22/7 xx 7 xx 7`

= 22 × 7

= 154 cm²

Area of quarter circle = `1/4 xx 154`

Area of quarter circle = 38.5 cm² 

3. Area of semicircle DEG:

Diameter DE = `"AB"/2` = 7 cm,

So radius = `7/2` = 3.5 cm. 

Area of full circle = πr²

= `22/7 xx 3.5 xx 3.5`

= `22/7 xx 12.25`

= 38.5 cm² 

Area of semicircle = `1/2 xx 38.5` 

Area of semicircle = 19.25 cm² 

4. Area of remaining shaded part:

Shaded area = Area of rectangle – Area of quarter circle + Area of semicircle

= 98 – (38.5 + 19.25)

= 98 – 57.75

= 40.25 cm²

The area of the remaining shaded part of the rectangle is 40.25 cm².