Question: Work out the volume of the triangular prism shown below.
1.9 m
2.4 m
2.2 m
3 m
Not drawn accurately
top-center: triangular prism; the triangular cross-section has base 2.4 m and height 1.9 m, and the prism length is 3 m.Work out the volume of the triangular prism shown below.
1.9 m
2.4 m
2.2 m
3 m
Not drawn accurately
Graph/shape: A triangular prism is shown. The front triangular face has base 2.4 m and perpendicular height 1.9 m, and the prism length is 3 m. The slanted side of the prism is labeled 2.2 m. position_hint = center
1. **State the problem:** We need to find the volume of a triangular prism with a triangular cross-section base of $2.4$ m, height $1.9$ m, and prism length $3$ m.
2. **Formula for volume of a triangular prism:**
$$\text{Volume} = \text{Area of triangular base} \times \text{length of prism}$$
3. **Calculate the area of the triangular base:**
The area of a triangle is given by:
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
Substitute the values:
$$\text{Area} = \frac{1}{2} \times 2.4 \times 1.9$$
4. **Calculate the area:**
$$\text{Area} = \frac{1}{2} \times 2.4 \times 1.9 = 1.2 \times 1.9 = 2.28$$
5. **Calculate the volume:**
$$\text{Volume} = 2.28 \times 3 = 6.84$$
6. **Final answer:**
The volume of the triangular prism is
$$6.84\ \text{cubic meters}$$
This means the prism can hold $6.84$ cubic meters of space.