Volume of a prism is the amount of three-dimensional space it occupies, found by multiplying the area of its uniform cross-sectional base by the perpendicular length of the prism: . This includes rectangular, triangular, and other familiar prisms, with base area calculated from the appropriate two-dimensional formula and the result expressed in cubic units; the prism’s length is not necessarily the same as a dimension of the base.
A prism has the same cross-section all the way through. To find its volume, use
where:
The base does not have to be the bottom face. Choose the face whose area is easiest to calculate.
Example: A triangular prism has triangular bases with a base of and a perpendicular height of . The prism is long. Find its volume.
Step 1: Find the area of the triangular base.
The area of a triangle is
Substitute the triangle’s dimensions:
Step 2: Multiply the base area by the prism’s perpendicular length.
Therefore, the volume of the triangular prism is
Remember to use square units for area and cubic units for volume.
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