Math  /  Geometry

QuestionWhat is the volume of the triangular prism shown below? Give your answer in m3\mathrm{m}^{3} to 1 d.p1 \mathrm{~d} . \mathrm{p}.
Not drawn accurately

Studdy Solution

STEP 1

1. The triangular prism has a triangular base.
2. The base of the triangle is 2.6 2.6 meters.
3. The height of the triangle is 1.9 1.9 meters.
4. The length of the prism (depth) is 3 3 meters.
5. The slant height is not needed for volume calculation.

STEP 2

1. Calculate the area of the triangular base.
2. Recall the formula for the volume of a prism.
3. Substitute the calculated area and given length into the volume formula.
4. Calculate the volume and round to one decimal place.

STEP 3

Calculate the area of the triangular base using the formula for the area of a triangle:
Area=12×Base×Height \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
Substitute the given values:
Area=12×2.6m×1.9m \text{Area} = \frac{1}{2} \times 2.6 \, \text{m} \times 1.9 \, \text{m}
Calculate the area:
Area=12×4.94m2 \text{Area} = \frac{1}{2} \times 4.94 \, \text{m}^2 Area=2.47m2 \text{Area} = 2.47 \, \text{m}^2

STEP 4

Recall the formula for the volume of a prism:
V=Base Area×Length V = \text{Base Area} \times \text{Length}

STEP 5

Substitute the calculated area and given length into the volume formula:
V=2.47m2×3m V = 2.47 \, \text{m}^2 \times 3 \, \text{m}

STEP 6

Calculate the volume:
V=2.47m2×3m V = 2.47 \, \text{m}^2 \times 3 \, \text{m} V=7.41m3 V = 7.41 \, \text{m}^3
Round the volume to one decimal place:
V7.4m3 V \approx 7.4 \, \text{m}^3
The volume of the triangular prism is:
7.4m3 \boxed{7.4 \, \text{m}^3}

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