Question

The radius of circle is 6.5 centimetres. Asquare has the same are as this circle. The length of each side of square , in centimetre is?

Answer 1

Since the square has the same area as the circle, it might help
if we look at the area of the circle first.

The area of any circle is      Area = (pi) x (radius)² .

Leave it in that form for just a second .  (Oh, this is going to be so easy . . .)

The area of a square is  (length of a side)² .

The problem says that the areas are equal.  So . . .

(length of each side)² = (pi) x (radius)²

Take the square root of each side of the equation:

Length of each side of the square = (radius of the circle) times ( √pi )

Length of each side = (6.5 centimeters) times ( √pi ) = 11.52 centimeters (rounded)