In given figure ABPC is a quadrant of a circle of radius 14 cm

In given figure ABPC 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.

Answer

We know, AC = r

In Δ ACB,

BC2 = AC2 + AB2

BC = AC√2 (Since, AB = AC)

BC = r√2

Required area = ar(Δ ACB) + ar(semicircle on BC as diameter) – ar(quadrant ABPC)

= (½ × r × r) + (½ × π × (r√2/2)2) – (¼ × π × r2)

= r2/2 + πr2/4 – πr2/4

= r2/2

= 196/2 cm2

= 98 cm2