The image presents a right triangular prism with the dimensions of its triangular base and height specified. Let's calculate the volume of the prism step by step.

Information from the image:

• The base of the triangle (AB) = 10 cm
• The height of the triangle (AC) = 8 cm
• The height of the prism (DE or EF) = 15 cm

Formula to find the volume of a triangular prism:

$\text{Volume} = \text{Area of the triangular base} \times \text{Height of the prism}$

Step 1: Find the area of the triangular base

The triangular base is a right triangle, so its area is calculated as: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 8 \, \text{cm} = 40 \, \text{cm}^2$

Step 2: Calculate the volume

Now, using the height of the prism (15 cm): $\text{Volume} = 40 \, \text{cm}^2 \times 15 \, \text{cm} = 600 \, \text{cm}^3$

Answer:

The volume of the triangular prism is 600 cm³. However, this value doesn't match any of the provided options. It seems there might be an issue with the provided options or the dimensions, as none of the choices (240 cm³, 180 cm³, 300 cm³, 360 cm³) corresponds to this calculation.

Would you like more details, or to review any steps?

Here are 5 related questions to extend your understanding:

1. How do you find the surface area of a triangular prism?
2. What changes in the volume if the height of the prism is doubled?
3. How can we verify that the triangle is a right triangle using its dimensions?
4. What is the relation between volume and mass if the density is given?
5. How do you calculate the volume of a prism with a non-right triangular base?

Tip: Always recheck your measurements to avoid dimensional misinterpretations!