The given problem involves finding the base length of the triangular cross-section of a triangular prism with a known volume.

Step 1: Recall the volume formula for a triangular prism.

The volume $V$ of a triangular prism is calculated using the formula: $V = \text{Area of Cross Section} \times \text{Length of the Prism}$ Where:

• The volume $V$ is given as 396 cm³.
• The length of the prism (which is the height of the triangular face) is 18 cm.
• The area of the cross-section is that of a right-angled triangle.

Step 2: Determine the area of the triangular cross-section.

The area $A$ of the triangular cross-section is: $A = \frac{1}{2} \times \text{base} \times \text{height}$ Here, the base of the triangle is the unknown value we need to find, and the height of the triangle is given as 11 cm.

Step 3: Use the volume formula.

Now, using the volume formula: $396 = \left(\frac{1}{2} \times \text{base} \times 11\right) \times 18$

Step 4: Solve for the base.

First, simplify the equation: $396 = 9 \times \text{base} \times 11$ $396 = 99 \times \text{base}$ Now, solve for the base: $\text{base} = \frac{396}{99} = 4 \, \text{cm}$

So, the base length of the triangular cross-section is 4 cm.

Would you like more details or further clarification on this problem?

Here are some related questions you can explore:

1. How do you calculate the volume of a cylinder?
2. What is the difference between the volume of a cone and a pyramid?
3. How do you calculate the surface area of a triangular prism?
4. How do you find the volume of other 3D shapes like cubes or spheres?
5. What happens to the volume if the length of the prism is doubled?

Tip: Always double-check that the units are consistent when using formulas!