Question

find the volume of this triangular prism. be sure to include the correct unit in your answer. image of triangular prism with 10 m, 5 m, 7 m labels input box units: m, m², m³ buttons: undo, clear

Explanation:

Step1: Recall the formula for the volume of a triangular prism.

The volume \( V \) of a triangular prism is given by the formula \( V = \text{Area of the triangular base} \times \text{length of the prism} \). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Calculate the area of the triangular base.

The base of the triangle is \( 5 \, \text{m} \) and the height of the triangle is \( 7 \, \text{m} \). So, the area of the triangular base \( A \) is \( \frac{1}{2} \times 5 \times 7 \).

$$ A = \frac{1}{2} \times 5 \times 7 = \frac{35}{2} = 17.5 \, \text{m}^2 $$

Step3: Multiply the area of the base by the length of the prism.

The length of the prism (the distance between the two triangular bases) is \( 10 \, \text{m} \). So, the volume \( V \) is \( 17.5 \times 10 \).

$$ V = 17.5 \times 10 = 175 \, \text{m}^3 $$

Answer:

\( 175 \, \text{cubic meters} \) (or \( 175 \, \text{m}^3 \))