Find the volume of a triangular prism with a height of 5 cm and a base that is a regular triangle with sides o

Question

Find the volume of a triangular prism with a height of 5 cm and a base that is a regular triangle with sides of 3 cm.

Answer 1

The area of a triangular prism of base area A and height H is just AH.

In a regular triangle all sides are the same length. The area of the base A can be found by multiplying the base of the triangle (3) by the triangle height (which is SQRT(3^2 - (3/2)^2) or SQRT(27/4). The base is two triangles of sides 3/2, 3 and SQRT(3^2 - (3/2)^2).

So area of base A = 3*SQRT(27/4) = 9SQRT(3)/2
A = 7.794

Volume = A*H = 7.794 * 5 = 38.971

Answer 2

First, find the cross sectional area, (the equilateral triangle) found by 1/2*b*h = 1/2*3*(sin 60 *3) = 3.897... Multiply by the height to get the volume, = 5*3.897.... = 19.4856 cm3 - is this o.k. ? I think the previous answer gave the base area as equal to a rectangle of lenths 3 and h (=2.59.... ), not a triangle, which will be half of this value!