Math CentralQuandaries & Queries


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.

Stephen La Rocque.

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