What is the volume of a triangular prism that has a height of \( 6 \mathrm{in} . \), a triangular base that measures 8 in . on each side, and a height of \( 6.93 \mathrm{in} . ? \)

To find the volume of a triangular prism, we can use the formula: \[ \text{Volume} = \text{Base Area} \times \text{Height} \] Given: - Height of the prism = 6 in - Triangular base with each side measuring 8 in - Height of the triangular base = 6.93 in First, we need to calculate the area of the triangular base. The formula for the area of a triangle is: \[ \text{Area of a triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} \] Given that the base of the triangle is 8 in and the height is 6.93 in, we can calculate the area of the triangular base. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}\times 8\times 6.93\) - step1: Multiply the terms: \(4\times 6.93\) - step2: Multiply the numbers: \(27.72\) The area of the triangular base is \(27.72 \, \text{in}^2\). Now, we can calculate the volume of the triangular prism using the formula: \[ \text{Volume} = \text{Base Area} \times \text{Height} \] Substitute the values we have: - Base Area = 27.72 in² - Height = 6 in Let's calculate the volume. Calculate the value by following steps: - step0: Calculate: \(27.72\times 6\) - step1: Multiply the numbers: \(166.32\) The volume of the triangular prism is \(166.32 \, \text{in}^3\).