Question

find the lateral area of the prism. the base is a regular octagon. 6 in. 15 in. square inches

Explanation:

Step1: Recall lateral area formula for prism

The lateral area \( LA \) of a prism is given by the formula \( LA = P \times h \), where \( P \) is the perimeter of the base and \( h \) is the height (or length) of the prism.

Step2: Find the perimeter of the regular octagon base

A regular octagon has 8 equal sides. Each side is given as 6 inches. So the perimeter \( P \) of the regular octagon is \( P = 8 \times \text{side length} \).
Substituting the side length (\( 6 \) inches) into the formula, we get \( P = 8 \times 6 = 48 \) inches.

Step3: Calculate the lateral area

We know the height \( h \) of the prism is 15 inches. Using the lateral area formula \( LA = P \times h \), substitute \( P = 48 \) inches and \( h = 15 \) inches.
So \( LA = 48 \times 15 = 720 \) square inches.

Answer:

720