What is the perimeter of a square which circumscribes a circle of radius a cm?

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Solution

When a square circumscribes a circle, the radius of the circle is half the length of the square.
Therefore if the radius of the circumscribed circle is a, the diameter will be 2a. It is this diameter that is equal to the length of the square.
Therefore the length of the square is 2a cm.

The area of a square is 4 × length
= 4 × 2a cm
= 8a cm

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