Question

How do we find the volume of a triangular pyramid ?

Answer 1

Use the formula for the volume of a triangular pyramid: `V = 1/3Ah`, where A = area of the triangular base, and H = height of the pyramid.

Explanation:

Let's take an example triangular pyramid and try this formula out. Let's say the height of the pyramid is 8, and the triangular base has a base of 6 and a height of 4.

First we need `A`, the area of the triangular base. Remember that the formula for the area of a triangle is `A=1/2bh`.
(Note: don't get this base confused with the base of the whole pyramid- we'll get to that later.)

So we just plug in the base and height of the triangular base:

`A=1/2*6*4`
`A=12`

Okay now we plug this area `A` and the height of the pyramid (8) for `h` in the main formula for the volume of a triangular pyramid, `V = 1/3Ah`.
`V = 1/3*12*8`.
`V=32`

There we go- now if you're given area of the triangular base it's even easier, just plug it and the pyramid height directly into the formula.