The radius of a circle is 6.5 centimeters. A square has the same area as this circle. What is the length of each side of the square, in centimeters?

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)

Answered by AL2006 | 2024-06-10

The area of the circle with a radius of 6.5 cm is approximately 132.73 cm². Therefore, the length of each side of a square with the same area is approximately 11.52 cm. This is found using the formulas for the area of both the circle and the square, and rounding the answer to two decimal places.
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Answered by AL2006 | 2024-11-12