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Question

The area of the square inscribed in a semicircle is 2 cm2 . If the semi-circle is extended to a full circle, the area of the square inscribed in this circle is ___cm2.

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Solution


Area of square = 2cm2
Side of square = 2cm
Let r be the radius of the semicircle.
Then from the figure,
r2=(2)2+(22)2r2=2+(24)r2=52r=(52)

When the semicircle is extended to form a full circle, the diagonal of the square inscribed in it will be the diameter of the circle.
r=(52)So, diameter=2×(52)Diagonal of square=side×2side×2=2×(52)side×2=2×5side=5 Area of square = side2
Area=(5)2=5 cm2

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