How do we find the volume of a triangular pyramid ?

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How do we find the volume of a triangular pyramid ?

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Answer 1 · 2018-05-09T03:28:06

Use the formula for the volume of a triangular pyramid: $V = \frac{1}{3} A h$ $V = 1/3Ah$ , 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 $A$ $A$ , the area of the triangular base. Remember that the formula for the area of a triangle is $A = \frac{1}{2} b h$ $A=1/2bh$ .
(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:

$A = \frac{1}{2} \cdot 6 \cdot 4$ $A=1/2*6*4$
$A = 12$ $A=12$

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

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.

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How do we find the volume of a triangular pyramid ?

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