Question

this prism has a lateral area of 1,296 square centimeters. the base is an equilateral triangle. find the height of the prism. 18 cm centimeters

Explanation:

Step1: Recall lateral - area formula for prism

The lateral - area formula for a prism with a regular base 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: Calculate the perimeter of the equilateral - triangle base

Since the base is an equilateral triangle with side length $a = 18$ cm, the perimeter $P$ of the base is $P=3a$. So, $P = 3\times18=54$ cm.

Step3: Solve for the height of the prism

We know that $L = Ph$, and $L = 1296$ square centimeters, $P = 54$ cm. Rearranging the formula $h=\frac{L}{P}$. Substitute $L = 1296$ and $P = 54$ into the formula: $h=\frac{1296}{54}=24$ cm.

Answer:

24