Find the area of a circle if the area of the inscribed square is 36.

The area of a circle is calculated by f-le S = nR ^ 2 (in this case, R is the radius of the circumscribed circle)
There is a formula that connects the side of a regular polygon inscribed in a circle and the radius described around this polygon:
An = 2R × sin 180 / n, where Аn-side
polygon,
n is the number of its vertices
1) A4 = 2R × sin 180/4
A4 = 2R × sin 45 °
A4 = 2R × √2 / 2
A4 = R√2
2) Skv = A ^ 2
A = √36
A = 6
3) 6 = R√2
R = 3√2
4) Scr = n (3√2) ^ 2
Scr = 18
Answer: 18