Question

BOAX is a quadrant of a circle of radius 6 centimetre . AB is diameter of semi-circle ABY .find the area of shaded portion.

Answer 1

Hey Friend ✋✋✋

Area of quadrant = 1/4 × π × 6²

= 22 × 9 / 7

= 198/7 cm²

Area of triangle = ½ × b × h = ½ × 6² = 18 cm²/

Area of segment, x = 198/7 - 18 = 72/7


Area of semicircle ....

Diameter of semicircle = hypotenuse of ∆ BOA

So... Diameter = √(6² + 6²)

= √72

= 6√2 cm

Radius of semicircle = 3√2 cm


Area of semicircle =
$\frac{\pi {r}^{2} }{2}$


$= \frac{\pi {(3 \sqrt{2)} }^{2} }{2} \\ \\ = \frac{\pi(9 \times 2)}{2} \\ \\ = \frac{198}{7}$


Area of shaded region = 198/7 - 72/7

= 126/7= 18 cm²


Hope it helps