Question

Find the area of the shaded region in given figure, if AB=24cm , AC=7cm and 0 is the centre of the circle

Answer 1

Hi,

∠BAC = 90 (angle in a semicirlce is 90)

AB = 24cm and AC = 7cm

BC²=AC²+AB²

BC²=24²+7²

BC²=576+49

BC=√625 = 25cm

D=25cm
r=25/2cm

Area of the semicircle = 1/2πr²
= 1/2 x 22/7 x 25/2 x 25/2
= 6875/28 = 245.53cm²

Now, Area of Triangle = 1/2xbxh
=1/2 x 7 x 24 = 7 x 12 = 84cm²

Area of the shaded portion = Area of Semicircle - Area of the Triangle
= 245.53 - 84 = 161.53cm²

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Answer 2

Given :   AC = 7cm AB  = 24cm and O is the Centre of the circle  

To Find :  area of the shaded region

Solution:

AC = 7 Cm

AB = 24 cm

BC is Diameter as it passes through O center of circle

Hence ∠BAC right angle

=> BC² = AB² + AC²  = 24² + 7²

=> BC = 25  cm

Diameter = 25 cm

Radius = 25/2 cm

Area of Semicircle = (1/2) π (25/2)²   =  625π/8  = 245.4  cm²

Area of Right angle = (1/2) *24* 7  = 84 cm²

area of the shaded region  = 245.4 - 84  =  161.4 cm²

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