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Question 7
In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region.
(use π=3.14)


Solution

Given: AC = 6 cm and AB = 8cm

We know that, triangle in a semi – circle with hypotenuse as diameter is right angled triangle.

A=90

In right angled ΔACB, use Pythagoras Theorem

BC2=AC2+BA2

BC2=62+82=36+64

BC2=100

BC=10 cm  [ Since length of a side cannot be negative]

Area of ΔABC=12×AB×AC=12×8×6=24 cm2

Here, diameter of circle, AB = 10 cm

Radius of circle r=102=5 cm

Area of circle =pir2=3.14×(5)2

=3.14×25=78.5 cm2

Area of the shaded region = Area of circle - Area of ΔABC

78.524=54 cm2

 

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