A square is inscribed in a circle of radius 5 cm. Find the area of the square.

Step-by-step solution

1. The diagonal of the square equals the diameter of the circle: $d=2\times 5=10$ cm.
2. Use diagonal formula for a square: $d=ssqrt2$.
3. Solve for side: $s=d/\sqrt{2}=10/\sqrt{2}=5\sqrt{2}$ cm.
4. Area of square: $A=s^2=(5\sqrt{2}{)}^2=25\times 2=50$ cm².
5. Thus the area of the square is $50$ cm².

Concept tested: Area of inscribed square

Published 1 October 2026 · How this solution was prepared and checked