https://r2.erweima.ai/mathbot/image/1726721401125ozbmhqow.jpg

To calculate the volume of the triangular prism shown in the image, we need to use the formula for the volume of a prism:

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

1. **Base Area**: Since the base of the prism is a triangle, we can find its area using the formula for the area of a triangle:

\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]

From the image, the base of the triangle is given as **6 mm** and the height of the triangle is **3 mm**.

\[
\text{Base Area} = \frac{1}{2} \times 6 \times 3 = 9 \, \text{mm}^2
\]

2. **Height of the Prism**: The height of the prism (the length between the triangular bases) is **10 mm**.

3. **Volume**: Now, we multiply the base area by the height of the prism:

\[
V = 9 \times 10 = 90 \, \text{mm}^3
\]

Thus, the volume of the triangular prism is **90 mm³**.

Would you like any more details on this? 

Here are some follow-up questions to explore this topic further:
1. How does the volume change if the base of the triangle increases?
2. What is the surface area of the triangular prism?
3. How can the formula for the volume of a prism be applied to other shapes?
4. If the height of the prism doubles, how will the volume be affected?
5. How would the volume change if the triangular base was equilateral instead?

**Tip:** Always make sure the dimensions used in your formula are consistent, especially when working with mixed units like millimeters and centimeters.

The volume of the triangular prism is ____ mm³. The prism has a triangular base with a base length of 6 mm, a height of 3 mm, and a prism height of 10 mm.

Learn how to calculate the volume of a triangular prism with a base of 6 mm, height of 3 mm, and a prism height of 10 mm. Detailed solution covering geometry concepts and the volume formula for prisms, suitable for students in Grades 6-8.

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