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| Math Central | Quandaries & Queries |
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Question from Melissa, a parent: What is the square footage of a 7'3" square octagon with a height of 5 inches? I need to know how much pea gravel to buy for my sons gravel pit. |
Hi Melissa.
If you look at this link you will find that the area of an octagon that measures "w" between the
parallel sides is A = w2 - 2[w / (2 + √2) ]2.
So for 7' 3", that's w = 7.25 feet, and my calculator says:
7.252 - 2(7.25 / [2 + √2] )2 = 43.54 square feet
which is reasonable, because the octagon would have less area than a 7.25 x 7.25 foot square, which would be a bit more than 50.
The depth you indicated is 5/12 of a foot. So we multiply 43.54 x (5/12) = 18.14 cubic feet.
That's how much gravel you'll need. A bit more than 18 cubic feet.
Cheers,
Stephen La Rocque.
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