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,
$\mathrm{Area}\mathrm{of}\mathrm{square}=\frac{1}{2}{d}^2=\frac{1}{2}{\left(2r\right)}^2=2r^2\mathrm{sq}\mathrm{units}$
Hence, the area of the square ABCD is 2r² sq units.