Question

A square ABCD is inscribed in a circle of radius r. Find the area of the square.

Answer 1

Let the diameter of the square be d and having circumscribed circle of radius r.
We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.
∴ d = 2r
Now,

Area of square`=1/2"d"^2 = 1/2(2"r")^2=2"r"  "sq"` units 

Hence, the area of the square ABCD is 2r² sq units.