Circumference 45. Find the area of a square inscribed in this circle.

If the circumference is 45, then we find the length of the radius:
l = 2pR => R = l / 2p.
R = 45 / 2p = 22.5 / p.
The length of the diameter of the circle will be equal to the length of the diagonal of the square inscribed in this circle, then we denote the length of the side of the square as x and write the following:
x ^ 2 + x ^ 2 = (45 / 2n) ^ 2;
2x ^ 2 = 2025 / (4 * n ^ 2);
x ^ 2 = 2025 / (8 * n ^ 2);
x = 45 / (2p√2).
Square area:
x ^ 2 = 2025 / 8n ^ 2 cm2.
Answer: 2025 / 8n ^ 2 cm2.