Question

1. A landscape architect used the entire length of a 75-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 flowerbed in the shape of a circle. (The drawing below are not to scale.) Perimeter = 75 feet Circumference = 75 feet a. Find the area of each flowerbed. Use 3.14 for . b. Which shape flower bed has the greater area? c. How many square feet greater is the area of the larger flower bed?

Answer 1

Answer:

a. the area of the square is 351.56 ft ^ 2

the area of the circumference is 447.65 ft ^ 2

b. the circumference has a greater area.

c. 96.02 ft ^ 2

Step-by-step explanation:

We have the following information:

Square perimeter: 75 ft

Circle perimeter: 75 ft

Now we know that the perimeter of the square is:

Ps = 4 * s

we solve for s (side), and we have:

s = Ps / 4, replacing:

s = 75/4

s = 18.75

Now, we can calculate the area of the square, knowing that:

As = s ^ 2

As = 18.75 ^ 2

As = 351.56, therefore the area of the square is 351.56 ft ^ 2

Now we repeat the process for the circle, knowing that the perimeter of the circle is:

Pc = 2 * pi * r

we solve for r:

r = Pc / 2 * pi, replacing:

r = 75 / (2 * 3.14)

r = 11.94

now the circle area is:

Ac = pi * r ^ 2 ^, replacing:

Ac = 3.14 * 11.94 ^ 2

Ac = 447.65, therefore the area of the circumference is 447.65 ft ^ 2

b. The one with the shape of the circumference has a greater area.

c. 447.65 - 351.56 = 96.09

This means that the difference is 96.02 ft ^ 2