To find the volume of a triangular prism, you use the formula:
Volume=Area of triangular base×Length (height) of the prism\text{Volume}=\text{Area of triangular base}\times \text{Length (height) of the prism}Volume=Area of triangular base×Length (height) of the prism
Step-by-step process:
- Calculate the area of the triangular base
The area of a triangle is given by:
Area=12×base×height of the triangle\text{Area}=\frac{1}{2}\times \text{base}\times \text{height of the triangle}Area=21×base×height of the triangle
where the base and height are the dimensions of the triangular face.
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Identify the length (height) of the prism
This is the distance between the two triangular faces (not the height of the triangle). -
Multiply the base area by the length of the prism
Volume=(12×base×height of triangle)×length of prism\text{Volume}=\left(\frac{1}{2}\times \text{base}\times \text{height of triangle}\right)\times \text{length of prism}Volume=(21×base×height of triangle)×length of prism
Example:
If the triangular base has a base of 10 inches and height of 7 inches, and the length of the prism is 3 inches, then:
- Area of the base = 12×10×7=35\frac{1}{2}\times 10\times 7=3521×10×7=35 square inches
- Volume = 35×3=10535\times 3=10535×3=105 cubic inches
This gives the volume of the prism as 105 cubic inches
Additional notes:
- If you know the three sides of the triangle but not the height, you can use Heron's formula to find the area of the triangle before multiplying by the prism length.
- For triangles with two sides and an included angle, use the formula for area:
Area=12×a×b×sin(θ)\text{Area}=\frac{1}{2}\times a\times b\times \sin(\theta)Area=21×a×b×sin(θ)
then multiply by the prism length for volume
This method works for any triangular prism regardless of the triangle type.
