Question

determine the area of a circular enclosure and a square enclosure made with 56 meters of fence and comment. the area of a square enclosure created with 56 meters of fence is about 196 square meters. (do not round until the final answer. then round to the nearest whole number as needed.) the area of a circular enclosure created with 56 meters of fence is about do not round until the final answer. then round to the nearest whole number as needed.)

Explanation:

Step1: Find the side - length of the square

The perimeter of a square is $P = 4s$, where $P$ is the perimeter and $s$ is the side - length. Given $P = 56$ meters, then $s=\frac{P}{4}=\frac{56}{4}=14$ meters.

Step2: Calculate the area of the square

The area of a square is $A_{square}=s^{2}$. Substituting $s = 14$ meters, we get $A_{square}=14^{2}=196$ square meters.

Step3: Find the radius of the circle

The circumference of a circle is $C = 2\pi r$, where $C$ is the circumference and $r$ is the radius. Given $C = 56$ meters, then $r=\frac{C}{2\pi}=\frac{56}{2\pi}=\frac{28}{\pi}$ meters.

Step4: Calculate the area of the circle

The area of a circle is $A_{circle}=\pi r^{2}$. Substituting $r = \frac{28}{\pi}$ meters, we have $A_{circle}=\pi\times(\frac{28}{\pi})^{2}=\pi\times\frac{784}{\pi^{2}}=\frac{784}{\pi}\approx\frac{784}{3.14}\approx249.7$ square meters.

Answer:

The area of the square enclosure is 196 square meters and the area of the circular enclosure is about 250 square meters (rounded to the nearest whole number).