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Question
In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Solution
Let a be the side of square.
∴ Diameter of a circle = Diagonal of the square = 8 cm
In right angled triangle ABC,
Using Pythagoras theorem,
(AC)2 = (AB)2 + (BC)2
∴ (8)2 = a2 + a2
64 = 2a2
a2 = 32
Hence,
Area of square = a2
= 32 cm2
∴ Radius of the circle = `"Diameter"/2`
∴ Area of the circle = πr2
= π(4)2
= 16 cm2
Therefore, the area of the shaded region = Area of circle – Area of square
The area of the shaded region = 16π – 32
= `16 xx (22/7) - 32`
= `128/7`
= 18.286 cm2
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