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What is the area of a square inscribed in a circle of diameter $x cm ?$

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2 x c m^{2}

2 x^{2} c m^{2}

4 x c m^{2}

x^{2} c m^{2}

answer is A.

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Detailed Solution

Given that, radius of circle

= xcm

We know that, the area of the square is (side)

2

.
Diameter

= 2 xcm

Diameter of circle = diagonal of square

⇒ Diagonal of square = 2 xcm

Area of square = (diagonal) 2 2

\Rightarrow

Area of square = (2 x) 2 2

⇒ 4 x 2 2 ⇒ 2 x 2 c m

Therefore, the area of a square inscribed in a circle of diameter

x cm

2 x 2 cm 2

.
Hence the correct option is 1.

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