The figure below is made up of two identical triangular prisms. What is the volume of the figure?

10 in.
6 in.
5 in.
6 in.
10 in.

1 answer

To find the volume of the figure made up of two identical triangular prisms, we first need to calculate the volume of one triangular prism and then multiply by two.

Step 1: Determine the area of the triangular base

The dimensions given suggest that the triangle has a base of 10 inches and a height of 6 inches. The area \( A \) of a triangle is calculated using the formula:

\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

Substituting the known values:

\[ A = \frac{1}{2} \times 10 , \text{in.} \times 6 , \text{in.} = \frac{1}{2} \times 60 = 30 , \text{in}^2 \]

Step 2: Determine the height of the prism

The height of the prism is given as 5 inches.

Step 3: Calculate the volume of one triangular prism

The volume \( V \) of a prism is given by the formula:

\[ V = \text{Base Area} \times \text{Height} \]

Substituting the area of the triangular base and the height:

\[ V = 30 , \text{in}^2 \times 5 , \text{in.} = 150 , \text{in}^3 \]

Step 4: Calculate the volume of the two prisms

Since the figure consists of two identical triangular prisms, the total volume \( V_{\text{total}} \) is:

\[ V_{\text{total}} = 2 \times 150 , \text{in}^3 = 300 , \text{in}^3 \]

Thus, the volume of the figure is:

\[ \boxed{300 , \text{in}^3} \]