Math Is Fun Forum

cmjames

Member

Registered: 2005-06-14

Posts: 1

Volume

Could someone please tell me how to work out the volume of an equilateral triangle. Thanks

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Volume

A triangle is a flat (2-dimensional) shape, and so would only have an area.

It is easy to work out the area of any triangle - if the triangle is positioned so that it's lower edge is horizontal, then the Area is the length of that edge (called the "base") multiplied by the height of the triangle, then halved:

A = bh/2

I have a page where you can calculale the area of several different shapes here

NOW, an equilateral triangle is a special case. Because all sides are equal, then the angles will all be 60 degrees, so the height can be worked out if you simply know the base length.

h = b sin 60

And sin 60 = sqrt(3)/2

so h = b * sqrt(3)/2

And so the area can be figured out if you simple know the length

A = bh/2 = b * b * sqrt(3)/2 /2 = b^2 * sqrt(3)/4

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mycalsuite

Member

Registered: 2025-09-10

Posts: 77

Website

Re: Volume

Since an equilateral triangle is a two-dimensional object, it only has area rather than volume.

Use the following calculation to determine its area:

A = (√3/4) a^2

where a is a side's length.

To calculate the volume of a three-dimensional object that has an equilateral triangle as its base, such as a pyramid or triangular prism, you would multiply that area by the height (or depth) of the shape.

Last edited by mycalsuite (Yesterday 02:33:15)

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mycalsuite