Question

a circle is circumscribed about a square of 9 cm what is the area of its circumference
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Answer 1

Formula used to calculate the area of circumscribed square is:
2 * r2
where, r is the radius of the circle in which a square is circumscribed by circle.

How does this formula work?

Assume diagonal of square is d and length of side is a.

We know from the Pythagoras Theorem, the diagonal of a
square is √(2) times the length of a side.
i.e d2 = a2 + a2
d = 2 * a2
d = √(2) * a
Now,
a = d / √2

and We know diagonal of square that are Circumscribed by
Circle is equal to Diameter of circle.
so Area of square = a * a
= d / √(2) * d / √(2)
= d2/ 2
= ( 2 * r )2/ 2 ( We know d = 2 * r )
= 2 * r2
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