# The perimeter of the a square and the perimeter of a circle are equal. If both are 156 cm., what is the area of each? How much is their difference in the area?

1
by CarlPaolo

• Brainly User
2015-11-13T07:07:23+08:00
A.  To solve for the area of square, find its side from the given perimeter.

Perimeter of square = 4s          where s = side
156 cm = 4s

156 cm = 4s
4          4

side = 39 cm

Area of square = (side)²
Area = (39 cm)²
Area of the square = 1,521 sq. cm

B.  To solve for the area of the circle, find its radius from the given perimeter.
Perimeter of a circle = 2(π)(r)    where: π = pi or 3.14         r = radius
156 cm = 2 (3.14) (r)
156 cm = 6.28 r

156 cm = 6.28 r
6.26     6.28

r ≈ 24.84 cm

Area of Circle = (π)(r)²
Area = (3.14) (24.84 cm)²
Area = (3.14) (617.03 cm²)
Area of the circle = 1,937.47 sq cm.

The difference between the areas of circle and square:
1,937.47 sq. cm - 1,521 sq. cm = 416.47 sq cm.

Final Answer:   The difference in their areas is 416.47 sq. cm.

This way further gives me understanding in analyzing other problems similar to this.