Question

A square has 98 sq cm area. What will be area of circle passing through its vertices .

Answer 1

Area of a sphere is related to it's sides as

s^2 = A

Thus s = ✓98 = 7✓2 cm

Now when you imagine a circle passing through a square's vertices, you will find that the circle's diameter is the same as the square's diagonal.

Thus length of diagonal of a square
d = s×✓2 = 14 cm

Thus the diameter is 14cm. Hence the radius is 7cm.

Thus area of the circle =

πr^2 = 3.14×49 = 153.86 sq cm

Answer 2

let side length be l
l2 = 98
l=root 98
The circle passing through the vertices will have its diameter along the diagonal of the square
Therefore diagonal = l root2 = root 98*2 = 14
Now area of circle = pie d^2 / 4
= 3.14 * 14*14/4
= 153.86