Triangular Prism Volume Worksheets - Free Printable

To calculate the volume of these shapes, we need to identify that they are all triangular prisms.

The formula for the volume of a triangular prism is:
$$ \text{Volume} = \text{Area of Base Triangle} \times \text{Length of Prism} $$

Where:
* $\text{Area of Base Triangle} = \frac{1}{2} \times \text{base} \times \text{height}$
* The "Length of Prism" is the distance connecting the two triangular faces (often labeled as the depth or length).

Let's solve each problem step-by-step.

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Problem 1:
* Triangle Base ($b$): $10\text{ in}$
* Triangle Height ($h$): $6\text{ in}$ (This is the perpendicular height inside the triangle)
* Prism Length ($l$): $8\text{ in}$

1. Calculate Area of Base: $\frac{1}{2} \times 10 \times 6 = 30\text{ sq in}$
2. Calculate Volume: $30 \times 8 = 240\text{ cu in}$

Answer 1: $240\text{ in}^3$

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Problem 2:
* Triangle Base ($b$): $9\text{ in}$
* Triangle Height ($h$): $7\text{ in}$
* Prism Length ($l$): $6\text{ in}$

1. Calculate Area of Base: $\frac{1}{2} \times 9 \times 7 = 31.5\text{ sq in}$
2. Calculate Volume: $31.5 \times 6 = 189\text{ cu in}$

*(Note: The measurement $11.4\text{ in}$ is the slant height and is not needed for volume calculation.)*

Answer 2: $189\text{ in}^3$

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Problem 3:
* Triangle Base ($b$): $10\text{ m}$
* Triangle Height ($h$): $8\text{ m}$
* Prism Length ($l$): $6\text{ m}$

1. Calculate Area of Base: $\frac{1}{2} \times 10 \times 8 = 40\text{ sq m}$
2. Calculate Volume: $40 \times 6 = 240\text{ cu m}$

*(Note: The measurement $11.2\text{ m}$ is extra information.)*

Answer 3: $240\text{ m}^3$

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Problem 4:
* Triangle Base ($b$): $12\text{ m}$
* Triangle Height ($h$): $11\text{ m}$
* Prism Length ($l$): $9\text{ m}$

1. Calculate Area of Base: $\frac{1}{2} \times 12 \times 11 = 66\text{ sq m}$
2. Calculate Volume: $66 \times 9 = 594\text{ cu m}$

*(Note: Measurements $13.4\text{ m}$ and $14.2\text{ m}$ are extra information.)*

Answer 4: $594\text{ m}^3$

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Problem 5:
* Triangle Base ($b$): $9\text{ m}$
* Triangle Height ($h$): $10\text{ m}$
* Prism Length ($l$): $10\text{ m}$

1. Calculate Area of Base: $\frac{1}{2} \times 9 \times 10 = 45\text{ sq m}$
2. Calculate Volume: $45 \times 10 = 450\text{ cu m}$

*(Note: Measurements $10.2\text{ m}$ and $14.4\text{ m}$ are extra information.)*

Answer 5: $450\text{ m}^3$

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Problem 6:
* Triangle Base ($b$): $10\text{ m}$
* Triangle Height ($h$): $6\text{ m}$
* Prism Length ($l$): $8\text{ m}$

1. Calculate Area of Base: $\frac{1}{2} \times 10 \times 6 = 30\text{ sq m}$
2. Calculate Volume: $30 \times 8 = 240\text{ cu m}$

*(Note: Measurement $11.7\text{ m}$ is extra information.)*

Answer 6: $240\text{ m}^3$

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Final Answer:
1. 240 in³
2. 189 in³
3. 240 m³
4. 594 m³
5. 450 m³
6. 240 m³