Question: Calculate the volume of the right-angled triangular prism shown below. Give your answer to 1 d.p. with the correct units. 21 m 37 m 15 m Not drawn accurately Graph/shape description: A right-angled triangular prism is shown in the lower center of the page, with the right angle marked at the upper-left triangle vertex; the triangle includes a side labeled 21 m, the prism length is labeled 15 m near the bottom-right edge, and a slanted edge on the right face is labeled 37 m.
1. **State the problem:** We need to calculate the volume of a right-angled triangular prism with given side lengths.
2. **Identify the dimensions:** The prism has a triangular base with sides $21\text{ m}$ and $37\text{ m}$ (hypotenuse), and the prism length (height) is $15\text{ m}$.
3. **Recall the formula for the volume of a prism:**
$$\text{Volume} = \text{Area of base} \times \text{length}$$
4. **Calculate the area of the triangular base:**
Since the triangle is right-angled, the two legs are perpendicular. One leg is $21\text{ m}$, and the other leg can be found using the Pythagorean theorem:
$$37^2 = 21^2 + b^2$$
$$1369 = 441 + b^2$$
$$b^2 = 1369 - 441 = 928$$
$$b = \sqrt{928} \approx 30.46\text{ m}$$
5. **Calculate the area of the triangle:**
$$\text{Area} = \frac{1}{2} \times 21 \times 30.46 = \frac{1}{2} \times 639.66 = 319.83\text{ m}^2$$
6. **Calculate the volume of the prism:**
$$\text{Volume} = 319.83 \times 15 = 4797.45\text{ m}^3$$
7. **Round the answer to 1 decimal place:**
$$\boxed{4797.5\text{ m}^3}$$
This is the volume of the right-angled triangular prism to 1 decimal place.