Question

this prism has a lateral area of 726 square meters. the base is an equilateral triangle. find the length of one side of the base. 22 m

Explanation:

Step1: Recall lateral area formula for prism

A triangular prism has 3 rectangular lateral faces. For a prism with base side length \( s \) and height (length of the prism) \( h \), the lateral area \( LA \) is \( LA = 3\times s\times h \) (since the base is an equilateral triangle, all 3 sides are equal, so 3 rectangles each with area \( s\times h \)).

Step2: Substitute known values

We know \( LA = 726 \) square meters and \( h = 22 \) meters. Plug into the formula: \( 726=3\times s\times22 \)

Step3: Solve for \( s \)

First, simplify the right - hand side: \( 3\times22 = 66 \), so the equation becomes \( 726 = 66s \). Then, divide both sides by 66: \( s=\frac{726}{66}=11 \)

Answer:

11