Question

this prism has a lateral area of 768 square inches. the base is a square. find the height of the prism. 12 in. inches

Explanation:

Step1: Find perimeter of base

Since the base is a square with side - length 12 inches, the perimeter $P$ of the square base is $P = 4s$, where $s = 12$ inches. So $P=4\times12 = 48$ inches.

Step2: Use lateral - area formula

The lateral - area formula for a prism is $L = Ph$, where $L$ is the lateral area, $P$ is the perimeter of the base, and $h$ is the height. We know that $L = 768$ square inches and $P = 48$ inches. Substituting these values into the formula gives $768=48h$.

Step3: Solve for height

To find $h$, we divide both sides of the equation $768 = 48h$ by 48. So $h=\frac{768}{48}=16$ inches.

Answer:

16