Which expression represents the volume of a triangular prism with length l, width w, and height h?

Which expression represents the volume of a triangular prism with length l, width w, and height h?

• A. 1/2 l w h
• B. l w h
• C. 1/3 l w h
• D. 2 l w h

Answer: (A)

Volume of a prism is found by multiplying the area of its base by how far it extends (the length). In a triangular prism, the base is a triangle. The area of a triangle is one-half of its base times its height, so with base w and height h, the base area is (1/2) w h. Multiply that by the length l to get the full volume: (1/2) w h × l, which is (1/2) l w h. This shows why the triangular prism has half the volume of a rectangular prism with the same l, w, and h.

Volume of a prism is found by multiplying the area of its base by how far it extends (the length). In a triangular prism, the base is a triangle. The area of a triangle is one-half of its base times its height, so with base w and height h, the base area is (1/2) w h. Multiply that by the length l to get the full volume: (1/2) w h × l, which is (1/2) l w h. This shows why the triangular prism has half the volume of a rectangular prism with the same l, w, and h.