Question

question 16 (1 point)
each side of the pentagon below is 13 feet long. how much larger is the perimeter of
the pentagon than the perimeter of the rectangle?
a. 7 feet
b. 11 feet
c. 16 feet
d. 36 feet

Explanation:

Step1: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). Here, \(l = 24\) feet and \(w = 8\) feet. So, \(P_{rectangle}=2\times(24 + 8)=2\times32 = 64\) feet.

Step2: Calculate the perimeter of the pentagon

A pentagon has 5 sides. Each side of the pentagon is \(s = 16\) feet. The formula for the perimeter of a regular pentagon is \(P=5s\). So, \(P_{pentagon}=5\times16=80\) feet.

Step3: Find the difference in perimeters

Subtract the perimeter of the rectangle from the perimeter of the pentagon: \(P_{pentagon}-P_{rectangle}=80 - 64=16\) feet.

Answer:

C. 16 feet