Question

In the given figure o is the centre of the circle aob is diameter ac=12 cm and BC = 16 cm . Find the area of the shaded region

Answer 1

Step-by-step explanation:

AC = 12 cm

BC = 26 cm

AB = ?

as AB is diameter, angle ACB = 90°

By pythogoras theorem,

AB² = AC² + BC²

AB² = 12x12 + 16x16

AB² = 144 + 256

AB = √400

AB = 20 cm

Radius = OA = 20/2

= 10 cm

Now,

Area of semicircle = ½πr²

= ½ × 22/7 × 10²

= 11 /7 × 100

= 1100/7

= 1571.4 cm²

Area of triangle = ½ × b × h

= ½ × 12 × 16

= 96 cm²

Ar of Shaded region = Ar of semicircle - Ar of triangle

= 1571.4 - 96

= 1475.4 cm²

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