Question

find the lateral area of the prism. the base is a regular pentagon. 9 in. 4 in. square inches

Explanation:

Step1: Recall lateral - area formula for prism

The lateral area \(L\) of a prism is given by \(L = Ph\), 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 - length sides. Given that the side length of the base pentagon \(s = 4\) inches, the perimeter \(P\) of the base is \(P=5s\). So, \(P = 5\times4=20\) inches.

Step3: Identify the height of the prism

The height \(h\) of the prism is given as \(h = 9\) inches.

Step4: Calculate the lateral area

Substitute \(P = 20\) inches and \(h = 9\) inches into the formula \(L = Ph\). We get \(L=20\times9 = 180\) square inches.

Answer:

180