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 calculate the area of the octagon, we'll divide it into 8 equal triangles:
Let the side of the octagon be x. We know that the length of the diagonal (d) is 100 feet. We can use the formula for the diagonal of a regular octagon:
d = (√2 + 1)x
100 = (√2 + 1)x
x = 100 / (√2 + 1)
x ≈ 38.2 feet
Now we have the side length of the octagon. To calculate the area of the octagon:
Area = 2 * (1 + √2) * s^2
Area = 2 * (1 + √2) * 38.2^2
Area ≈ 3687.8 square feet
Now, the total pounds of vegetables produced in the garden is 236 pounds per family, spread across 90 families. So total pounds produced = 236 * 90 = 21240 pounds.
To find the pounds of vegetables produced per square foot:
Pounds per square foot = Total pounds produced / Area
Pounds per square foot = 21240 / 3687.8
Pounds per square foot ≈ 5.8
Rounded to the nearest tenth, the pounds of vegetables produced per square foot is 5.8. None of the provided options match this calculation, so it seems like there was a misinterpretation or misstep in the question provided.