Question

a triangular prism has bases with three congruent sides, each measuring 4 feet. the height of each triangle is approximately 3.5 feet. the distance between the triangular bases is 7 feet. what is the lateral area of the prism? 73.5 feet 73.5 square feet 84 feet 84 square feet

Explanation:

Step1: Identify the formula for lateral - area of a triangular prism

The lateral - area \(L\) of a triangular prism is given by \(L = Ph\), where \(P\) is the perimeter of the base and \(h\) is the height (the distance between the bases).

Step2: Calculate the perimeter of the base

The base is an equilateral triangle with side length \(s = 4\) feet. The perimeter \(P\) of an equilateral triangle is \(P=3s\). So, \(P = 3\times4=12\) feet.

Step3: Calculate the lateral - area

The height \(h\) (distance between the bases) is \(h = 7\) feet. Using the formula \(L = Ph\), we substitute \(P = 12\) feet and \(h = 7\) feet. So, \(L=12\times7 = 84\) square feet.

Answer:

D. 84 square feet