https://file.aiquickdraw.com/mathbot/file/1730357175908jh6b5bag.jpg

To solve this problem, let's break down the steps:

### Step 1: Determine the area of the triangular base
The shape at the end of the prism is a right triangle with:
- One side measuring 8 cm (height).
- Another side measuring 5 cm (base).

The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Substituting the values:
\[
A = \frac{1}{2} \times 5 \, \text{cm} \times 8 \, \text{cm} = \frac{1}{2} \times 40 = 20 \, \text{cm}^2
\]

### Step 2: Use the volume formula to find the length of the prism
The volume \( V \) of a prism is given by:
\[
V = A \times L
\]
where:
- \( V = 400 \, \text{cm}^3 \) (given),
- \( A = 20 \, \text{cm}^2 \) (area of the base),
- \( L \) is the length of the prism we need to find.

Rearrange the formula to solve for \( L \):
\[
L = \frac{V}{A} = \frac{400 \, \text{cm}^3}{20 \, \text{cm}^2} = 20 \, \text{cm}
\]

### Answer
The length of the prism is \( 20 \, \text{cm} \).

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Would you like more details on any step or have questions?

### Related Questions
1. What is the formula for the volume of different types of prisms?
2. How does the area of a base affect the overall volume of a prism?
3. If the base dimensions changed to 6 cm and 8 cm, what would the length be for the same volume?
4. How do we calculate the volume of a pyramid with a triangular base?
5. What would happen to the length if the volume was doubled?

### Tip
When working with volumes, ensure that all measurements (e.g., area and length) are in compatible units to avoid calculation errors.

If the volume of the prism is 400 cm³, find its length.

Find the length of a prism with a triangular base, given a volume of 400 cm³, base of 5 cm, and height of 8 cm. This problem involves calculating the area of a triangle and using the prism volume formula, suitable for students in Grades 7-9.

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