Question

Find the area of the shaded region where ABC is a quadrant of radius 5cm and a semicircle is drawn with BC as diameter.

Options

• 8.8 cm²

• 7.14cm²

• 12.5cm²

• 19.64cm²

Answer 1

12.5cm²

Explanation:

Area of the shaded region = Area of semicircle-Area of the segment of the sector BAC

Area of the semicircle with BC as diameter = `1/2 xx 22/7 xx 5/sqrt2 xx 5/sqrt2`

`= 19.64  "cm"^2` .....(i)

Area of segment = Area of quadrant – Area of ΔABC

`90/360 xx 22/7 xx 5^2 - 1/2 xx 5 xx 5`

`= 19.64 - 12.5`

`= 7.14  "cm"^2`....(ii)

Area of the shaded region = (i) – (ii)

`= 19.64 - 7.14`

`= 12.5  "cm"^2`