Math / Geometry

QuestionExample 3 Find the volume of the following triangular prisms 60

Studdy Solution

STEP 1

1. The base of the triangular face of the prism is 4 cm.
2. The height of the triangular face of the prism is 3 cm.
3. The length (or depth) of the prism is 8 cm.
4. The hypotenuse of the triangular face is 5 cm.
5. The volume of a triangular prism can be found by multiplying the area of the triangular base by the length of the prism.

STEP 2

1. Calculate the area of the triangular base.
2. Multiply the area of the triangular base by the length of the prism to find the volume.

STEP 3

Calculate the area of the triangular base using the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
Given: $\text{base} = 4 \, \text{cm}$ $\text{height} = 3 \, \text{cm}$
Thus: $\text{Area} = \frac{1}{2} \times 4 \, \text{cm} \times 3 \, \text{cm}$

STEP 4

Perform the multiplication to find the area of the triangular base: $\text{Area} = \frac{1}{2} \times 4 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2$

STEP 5

Multiply the area of the triangular base by the length of the prism to find the volume: $\text{Volume} = \text{Area} \times \text{length}$ Given: $\text{Area} = 6 \, \text{cm}^2$ $\text{length} = 8 \, \text{cm}$
Thus: $\text{Volume} = 6 \, \text{cm}^2 \times 8 \, \text{cm}$

STEP 6

Perform the multiplication to find the volume: $\text{Volume} = 6 \, \text{cm}^2 \times 8 \, \text{cm} = 48 \, \text{cm}^3$
Solution: The volume of the triangular prism is $48 \, \text{cm}^3$ .

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