Math CentralQuandaries & Queries


Question from Mady, a student:
What is the general equation used to find the volume of a triangular prism?


The general expression is (Base area) times (height).

To find base area

triangle area = a x b x sin(C)/2

where a,b are the lengths of two edges, C the angle between them. If one angle of the base triangle is a right angle the area is just half the product of the neighboring sides, because

sin(90 degrees) = 1

If you know all three edges and no angles of a triangle, you can use the cosine law

a2 = b2 + c2 -2bc cos A

to find A, or more directly use Heron's formula

Good Hunting!


I want to add a footnote to RD's response. The expression volume = (Base area) times (height) is true for any prism not just triangular prisms. The expression also holds true if the prism is not a right prism as long as the height is the distance between the congruent, parallel polygons.

triangular prism


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