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**cmjames****Member**- Registered: 2005-06-14
- Posts: 1

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

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

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

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

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