Question

find the lateral area of the prism. the base is an equilateral triangle. 12 ft. 18 ft. square feet

Explanation:

Step1: Identify side - length of base and height of prism

The side - length of the equilateral - triangle base $s = 12$ ft and the height of the prism $h=18$ ft.

Step2: Recall the formula for lateral area of a prism

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

Step3: Calculate the perimeter of the equilateral - triangle base

For an equilateral triangle with side - length $s$, the perimeter $P = 3s$. Substituting $s = 12$ ft, we get $P=3\times12 = 36$ ft.

Step4: Calculate the lateral area

Substitute $P = 36$ ft and $h = 18$ ft into the formula $L = Ph$. So, $L=36\times18=648$ square feet.

Answer:

648