Question

find the lateral area of the prism. the base is a regular pentagon. 6 in. 2 in. square inches

Explanation:

Step1: Recall lateral - area formula for prism

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

Step2: Calculate the perimeter of the base

A regular pentagon has 5 equal sides. Given that the side - length of the base pentagon is $s = 2$ inches, the perimeter $P$ of the base is $P=5s$. Substituting $s = 2$ inches, we get $P = 5\times2=10$ inches.

Step3: Identify the height of the prism

The height of the prism $h = 6$ inches.

Step4: Calculate the lateral area

Using the formula $L = Ph$, substitute $P = 10$ inches and $h = 6$ inches. So, $L=10\times6 = 60$ square inches.

Answer:

60