Question

this prism has a lateral area of 1,125 square feet. the base is a regular pentagon. find the length of one side of the base. 15 ft. feet

Explanation:

Step1: Recall lateral - area formula

The lateral - area formula for a prism is $L = Ph$, where $L$ is the lateral area, $P$ is the perimeter of the base, and $h$ is the height of the prism.

Step2: Substitute known values

We know that $L = 1125$ square feet and $h=15$ feet. Substituting into the formula $L = Ph$, we get $1125 = P\times15$.

Step3: Solve for the perimeter $P$

Dividing both sides of the equation $1125 = P\times15$ by 15, we have $P=\frac{1125}{15}=75$ feet.

Step4: Find the side - length of the regular pentagon

Since the base is a regular pentagon and the perimeter of a regular pentagon is $P = 5s$, where $s$ is the side - length. We know $P = 75$ feet. Then $75 = 5s$.

Step5: Solve for the side - length $s$

Dividing both sides of the equation $75 = 5s$ by 5, we get $s = 15$ feet.

Answer:

15