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
Steps to calculate the volume:
- Find the area of the triangular base
The area of a triangle is generally given by:
Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}Area=21×base×height
where the base and height refer to the dimensions of the triangular face of the prism.
- Multiply the area of the triangle by the length of the prism
The length (sometimes called the height of the prism) is the distance between the two triangular bases.
Formula summary:
Volume=12×b×h×L\text{Volume}=\frac{1}{2}\times b\times h\times LVolume=21×b×h×L
- bbb = base of the triangle
- hhh = height of the triangle
- LLL = length (or height) of the prism (distance between the triangular faces)
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:
Volume=12×10×7×3=105 cubic inches\text{Volume}=\frac{1}{2}\times 10\times 7\times 3=105\text{ cubic inches}Volume=21×10×7×3=105 cubic inches
Notes:
- If you know the three sides of the triangular base instead of base and height, you can use Heron's formula to find the area of the triangle, then multiply by the length of the prism.
- If you know two sides and the included angle of the triangle, use trigonometry to find the area before multiplying by the length.
This method applies universally for any triangular prism
