Question
If Area of the square inscribed in a semicircle is 2cm2 .Find the area of the square inscribed in a full circle?
Answer: Option D
 - Area of square = 2cm2
Side of square = square root of 2
Let r be the radius of the circle and adjust it like that it forms a right angle triangle then
r2 = (square root of 2)2 + (square root of 2 / 2)2
r2 = 2 + ( 2 / 4)
r2 = 5 / 2
r = square root of ( 5 / 2)
In a full square the diagonal of square will be the diameter of the cirlcle.
r = square root of ( 5 / 2) is this so diameter = 2 x square root of (5 / 2)
Diagonal of square = side x square root of 2
side x square root of 2 = 2 x square root of 5 / square root of 2
side x 2 = 2 x square root of 5
side = square root of 5
Area of square = r2
= (square root of 5)2
= 5 cm2
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 - Area of square = 2cm2
Side of square = square root of 2
Let r be the radius of the circle and adjust it like that it forms a right angle triangle then
r2 = (square root of 2)2 + (square root of 2 / 2)2
r2 = 2 + ( 2 / 4)
r2 = 5 / 2
r = square root of ( 5 / 2)
In a full square the diagonal of square will be the diameter of the cirlcle.
r = square root of ( 5 / 2) is this so diameter = 2 x square root of (5 / 2)
Diagonal of square = side x square root of 2
side x square root of 2 = 2 x square root of 5 / square root of 2
side x 2 = 2 x square root of 5
side = square root of 5
Area of square = r2
= (square root of 5)2
= 5 cm2
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