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