Question

In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. [Use Π = 22/7]

Answer 1

As ABC is a quadrant of the circle, ∠BAC will be of measure 90º.

In ΔABC,

BC² = AC² + AB²

= (14)² + (14)²

BC = 14sqrt2

Radius (r₁) of semi-circle drawn on BC = `(14sqrt2)/2 = 7sqrt2 cm`

Area of ΔABC = 1/2 x AB x AC

= 1/2 x 14 x 14

= 98 cm²

Area of sector ABDC = `90^@/360^@ xx pir^2`

`= 1/4 xx 22/7 xx 14 xx 14`

=154 cm²

Area of semi circle drawn of BC = `1/2xxpixxr_1^2 = 1/2 xx 22/7 xx (7sqrt2)^2`

`= 1/2 xx 22/7xx 98 = 154 cm^2`

Area of shaded region =  Area of semi- circle - (Area of sector ABDC - Area of ΔABC) = 154 - (154-98)

= 98 cm²