A landscape architect used the entire length of an 80-foot rope to lay out a flower bed in the shape of a square. In another area, he used the entire length of the same rope to lay out a second flower bed in the shape of a circle. (Drawings not to scale.)

A landscape architect used the entire length of an 80ft rope to lay out a flower

bed in the shape of a square. In another area, he used the entire length of the

same rope to lay out a second flower bed in the shape of a circle.

Perimeter of square = 80 feet Circumference of circle = 80 feet

How many square feet greater is the area of one of the flower beds than the other? (use 3.14 for pi)

:

Area of the square: 20 * 20 = 400 sq/ft

:

Find the radius of the circle using the circumference:

2*3.14*r = 80

r = 80%2F6.28

r = 12.74 ft

:

Find the area of the circle using 13.03 as the radius

A = 3.14*12.74^2

A = 509.6 sq/ft

;

:

509.6 - 400 = 109.6 sq/ft more in the circle

Explanation: