Area of the circle = πr², so we need to find the radius of the circle.
Because the square is inscribed in the circle, the diameter of the circle is equal the diagonal of the square.
Using the Pythagorean theorem we can find the diagonal of the square, because this diagonal is going to be a hypotenuse of the triangle, that is formed when diagonal divides the square onto 2 triangles.
1) hypotenuse² =leg1² +leg2²= 10² +10²=2*10²,
hypotenuse = 10√2 cm, so
2) diagonal of the square = diameter of the circle = 10√2cm.
3) radius of the circle= diameter of the circle/2 =10√2/2 = 5√2 cm
4) Area of the circle = πr²= π*(5√2)² = 50π
Exact value of the Area of the circle = 50π cm²
5) Estimated value of the Area of the circle = 50π ≈ 157.1 cm²
