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 $20 \, \text{cm}$.

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.