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inwosu
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The perimeter of a hexagon is 24, what is the area 20 Oct 2007, 13:18
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The perimeter of a hexagon is 24, what is the area?



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beckee529
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The perimeter of a hexagon is 24, what is the area 20 Oct 2007, 13:35
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inwosu
The perimeter of a hexagon is 24, what is the area?
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i would approach it this way.
1) find the length of each side: 24/6 = 4
2) find out how many triangles are in the hexagon (from diagram): 6 equilateral
3) find the area of one and multiply by 6

a = 1/2 bh

b = 4
h = 2sqrt3

1/2 * 4 * 2sqrt3 = 4sqrt3

6a = 6 * 4sqrt3 = 24sqrt3
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The perimeter of a hexagon is 24, what is the area 20 Oct 2007, 13:41
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Now why do we have to use the sqrt of 3?
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The perimeter of a hexagon is 24, what is the area 20 Oct 2007, 13:49
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inwosu
Now why do we have to use the sqrt of 3?
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the 30-60-90 triangle ratio
30-60-90 = 1 : sqrt3 : 2

so in this case, if you take one triangle, have to split it in two to find the height (since we know the base is 4). so now we have a 30-60-90 triangle. the side that corresponds with 30 degree is 2 (base split in two), 60 degree is 2sqrt 3 (our height), and 90 degree is 4 (original exterior side of hexagon). hope that helps, i'll try to upload a diagram.



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