Question

find the volume of this triangular prism.
be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(5\) in and the height is \(5\) in. So, \(A = \frac{1}{2}\times5\times5=\frac{25}{2}\text{ in}^2\).

Step2: Find the volume of the triangular prism

The formula for the volume of a prism is \(V=A\times length\), where \(A\) is the area of the base and \(length\) is the length of the prism. The length of the prism is \(6\) in. Substitute \(A = \frac{25}{2}\text{ in}^2\) and \(length = 6\) in into the formula: \(V=\frac{25}{2}\times6\).

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Answer:

\(75\text{ in}^3\)