# How do you measure the area of a hexagon?

**URL:** <https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213>\
**Category:** Factual Questions\
**Created:** [May 11, 2000, 9:22am UTC](https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213 "2000-05-11T09:22:20Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![VarlosZ](https://avatars.discourse-cdn.com/v4/letter/v/d78d45/32.png) [@VarlosZ](https://boards.straightdope.com/u/VarlosZ)\
**Post date:** [May 11, 2000, 9:22am UTC](https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213/1 "2000-05-11T09:22:20Z")

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Can you do it using only the height, or distance between opposite sides? In case your wondering: yes, this question does spring from some stupid wargame where the map is broken into hexes. So, in other words, can you tell me how many square kilometers I’ve conquered in my make-believe escapist fantasies? Thanks.

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**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\
**Post date:** [May 11, 2000, 9:38am UTC](https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213/2 "2000-05-11T09:38:46Z")

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Yes, of course you only need one number. There aren’t different shapes of hexagons - only larger ones and smaller ones.

Easiest way (at least for me) to think about it is to notice that a hexagon is made up of six equilateral triangles. You say you know the distance between the two sides of the hexagon; we’ll call that L. The height of each triangle is L/2. The triangles have angles of 60 degrees, so the base of each triangle is (L/2) / tan(60) \* 2, or L/sqrt(3), because tan(60)=sqrt(3)/2. The area of each triangle is therefore L[sup]2[/sup]/(2 sqrt(3)). You’ve got six of those, so the total area is 3 L[sup]2[/sup]/sqrt(3), or sqrt(3)\*L[sup]2[/sup].

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**Author:** ![matt](https://avatars.discourse-cdn.com/v4/letter/m/a6a055/32.png) [@matt](https://boards.straightdope.com/u/matt)\
**Post date:** [May 11, 2000, 10:15am UTC](https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213/3 "2000-05-11T10:15:27Z")

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Oops, you forgot the area of a triangle is half the base X height.

So the total area is half sqrt(3)\*(L squared)

or 0.866 multiplied by (L squared)

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**Author:** ![UncleBeer](https://avatars.discourse-cdn.com/v4/letter/u/977dab/32.png) [@UncleBeer](https://boards.straightdope.com/u/UncleBeer)\
**Post date:** [May 11, 2000, 11:53am UTC](https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213/4 "2000-05-11T11:53:37Z")

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You guys, of course, are assuming the OP is referring to a _regular_ hexagon.

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**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\
**Post date:** [May 11, 2000, 12:26pm UTC](https://boards.straightdope.com/t/how-do-you-measure-the-area-of-a-hexagon/19213/5 "2000-05-11T12:26:45Z")

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Of course, the hexagon is regular, **Unc** , those board games have lots of roughage.