Answer:
The circle makes the larger area
The difference in the two areas is roughly 132.2479 square feet.
=================================================
Explanation:
If Carter decides to go for a circle, then 88 is the circumference, which is the distance around the circle (aka perimeter of the circle).
Use this to find the radius needed
C = 2*pi*r
r = C/(2pi)
r = 88/(2pi)
r = 44/pi
I'll leave it in exact form rather than approximate it.
Once we know the radius, we can find the area of the circle.
A = pi*r^2
A = pi(44/pi)^2
A = pi*(1936/(pi^2))
A = 1936/pi
A = 616.247939651819 approximately
I used my calculator's stored version of pi to compute the area in the final step.
We'll be comparing this number later, so hold onto it for now.
-------------------------------------
If Carter instead decides for a square, then 88 is the perimeter since it's the amount of fencing he has to work with.
Divide it into 4 pieces to find the length of each side of the square (all sides are equal in a square)
88/4 = 22
Each side is 22 feet
The area of this square is (22)^2 = 22*22 = 484 square feet
--------------------------------------
Summary:
- If Carter goes for a circular enclosure, then he gets roughly 616.2479 square feet.
- The square enclosure only gets him exactly 484 square feet.
The circle wins in terms of larger area.
The difference being roughly 616.2479 - 484 = 132.2479 square feet.
