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To calculate the volume of the right-angled triangular prism, we need to use the formula for the volume of a prism:

\[
V = \text{Area of the triangular base} \times \text{length (or height) of the prism}
\]

### Step 1: Calculate the area of the triangular base
The base is a right-angled triangle, and we can calculate its area using the formula:

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

From the diagram, the base of the triangle is 23 m, and the height (the perpendicular) is 11 m. So,

\[
\text{Area of triangle} = \frac{1}{2} \times 23 \times 11 = \frac{1}{2} \times 253 = 126.5 \, \text{m}^2
\]

### Step 2: Calculate the volume of the prism
The length (or height) of the prism is given as 38 m. So, the volume is:

\[
V = 126.5 \times 38 = 4807 \, \text{m}^3
\]

Thus, the volume of the prism is approximately **4807 cubic meters** (rounded to 1 decimal place as requested).

Would you like any further details or have any questions?

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Here are 5 related questions to deepen your understanding:
1. How would the volume change if the base of the triangle was increased by 5 meters?
2. What is the effect on volume if the height of the triangular base is doubled?
3. How would you find the surface area of this triangular prism?
4. Can you calculate the perimeter of the triangular base?
5. How would the volume change if the length of the prism was reduced by half?

**Tip:** Always ensure the units are consistent when calculating volume, especially for more complex shapes.

Calculate the volume of the right-angled triangular prism shown below. Give your answer to 1 d.p. and remember to give the correct units.

Learn how to calculate the volume of a right-angled triangular prism with a base of 23 m, height of 11 m, and prism length of 38 m. This step-by-step solution uses geometry formulas, including area of triangles and volume of prisms, suitable for students in Grades 9-11.

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