https://file.aiquickdraw.com/mathbot/file/17237648435864840i1fh.jpg

The figure in the image is a triangular prism. The volume of a triangular prism can be calculated using the formula:

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

### Step 1: Calculate the area of the triangular base.
The base of the triangle is \(6 \, \text{km}\), and the height of the triangle (perpendicular to the base) is \(8 \, \text{km}\). The area \(A\) of the triangular base is given by:

\[
A = \frac{1}{2} \times \text{Base} \times \text{Height}
\]

\[
A = \frac{1}{2} \times 6 \, \text{km} \times 8 \, \text{km} = 24 \, \text{km}^2
\]

### Step 2: Multiply by the height of the prism.
The height (or length) of the prism is \(9 \, \text{km}\). The volume \(V\) of the prism is:

\[
V = \text{Base Area} \times \text{Height} = 24 \, \text{km}^2 \times 9 \, \text{km} = 216 \, \text{km}^3
\]

### Final Answer:
The volume of the prism is \(216 \, \text{km}^3\).

Would you like more details or have any questions about this problem?

---

Here are 8 related questions to deepen your understanding:

1. What is the volume of a triangular prism with a different set of base and height dimensions?
2. How would the volume change if the height of the prism were doubled?
3. How do you find the volume of a prism with a different shaped base (e.g., rectangular)?
4. Can you calculate the surface area of this triangular prism?
5. What would the volume be if the base triangle was equilateral?
6. How do you derive the formula for the area of a triangle?
7. If the prism was tilted, would the volume calculation change?
8. What are some real-world applications of calculating the volume of prisms?

**Tip:** Always check if the triangle in the base is a right triangle when dealing with prisms; this simplifies the area calculation.

Learn how to calculate the volume of a triangular prism with a base area of 24 square kilometers and a height of 9 kilometers. Detailed step-by-step solution using the formula for volume of a triangular prism. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation