A community garden is in the shape of a regular octagon. The length of a diagonal of the garden is 100 feet.
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If ninety families plant and harvest an equal share of the garden producing 236 pounds of vegetables per family, how many pounds of vegetables are produced per square foot? Round to the nearest tenth.
30.0
3.0
1.2
0.3
To find the area of the octagon, we can divide it into 8 isosceles triangles. Each isosceles triangle can be further divided into 2 right triangles, with each right triangle having a base of 50 feet and a height of 50/sqrt(2) = 35.4 feet (since the diagonal is the hypotenuse of the right triangle).
Therefore, the area of each isosceles triangle is 0.5 * 50 * 35.4 = 885 square feet.
Since there are 8 isosceles triangles in the octagon, the total area of the octagon is 8 * 885 = 7080 square feet.
If 90 families are harvesting the garden and each family produces 236 pounds of vegetables, the total amount of vegetables produced is 90 * 236 = 21240 pounds.
To find the pounds of vegetables produced per square foot, we divide the total amount of vegetables produced by the total area of the octagon: 21240 / 7080 = 3 pounds of vegetables per square foot.
Therefore, the answer is 3.0 pounds per square foot.