Question

this prism has a lateral area of 864 square meters. the base is an equilateral triangle. find the length of one side of the base. 24 m meters

Explanation:

Step1: Recall lateral - area formula

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

Step2: Let the side - length of the equilateral triangle base be \(s\).

The perimeter \(P\) of an equilateral triangle with side - length \(s\) is \(P = 3s\). We know that \(L=864\) square meters and \(h = 24\) meters. Substitute into the lateral - area formula: \(864=3s\times24\).

Step3: Solve the equation for \(s\).

First, simplify the right - hand side of the equation: \(3s\times24 = 72s\). So, the equation becomes \(864 = 72s\). Then, divide both sides of the equation by 72: \(s=\frac{864}{72}\).

Step4: Calculate the value of \(s\).

\(\frac{864}{72}=12\).

Answer:

12