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)2⇒r2=2+(24)⇒r2=52⇒r=√(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×√2⇒side×√2=2×√(52)⇒side×2=2×√5⇒side=√5 Area of square = side2 ⇒Area=(√5)2=5 cm2

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