Question

tarek has 72 feet of plastic fencing to make a flower garden in his backyard. the garden shape can either be circular or square. if he uses all of the fencing, what is the difference between the area of the circular garden and the square garden? use 3.14 for π. round to the nearest hundredth if necessary.

Explanation:

Step1: Find the side length of the square

The perimeter of the square is 72 feet. The formula for the perimeter of a square is \( P = 4s \), where \( s \) is the side length. So, \( s=\frac{P}{4}=\frac{72}{4} = 18 \) feet.

Step2: Calculate the area of the square

The formula for the area of a square is \( A_{square}=s^2 \). Substituting \( s = 18 \), we get \( A_{square}=18^2=324 \) square feet.

Step3: Find the radius of the circle

The circumference of the circle is 72 feet. The formula for the circumference of a circle is \( C = 2\pi r \), where \( r \) is the radius. Using \( \pi = 3.14 \), we have \( 72=2\times3.14\times r \). Solving for \( r \), \( r=\frac{72}{2\times3.14}=\frac{72}{6.28}\approx11.46 \) feet.

Step4: Calculate the area of the circle

The formula for the area of a circle is \( A_{circle}=\pi r^2 \). Substituting \( \pi = 3.14 \) and \( r\approx11.46 \), we get \( A_{circle}=3.14\times(11.46)^2\approx3.14\times131.33\approx412.38 \) square feet.

Step5: Find the difference in areas

Subtract the area of the square from the area of the circle: \( A_{circle}-A_{square}\approx412.38 - 324 = 88.38 \) square feet.

Answer:

\( 88.38 \)