https://file.aiquickdraw.com/mathbot/file/1728485862113vg8rmx76.jpg

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!

What is the volume of a prism with a right triangular base where the triangle has a base of 10 cm, height of 8 cm, and the prism height is 15 cm?

Learn how to calculate the volume of a right triangular prism with a triangular base of 10 cm by 8 cm, and a prism height of 15 cm. This problem covers the geometric formula for volume calculation and is suitable for students in Grades 7-9.

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