To find the area of the shaded region below, which consists of a square with a circle cut out of it, we can follow these steps:
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Find the area of the square: Since the diameter of the circle is 20 feet, the radius \( r \) of the circle is: \[ r = \frac{20}{2} = 10 \text{ feet} \] The side length of the square is equal to the diameter of the circle, which is 20 feet. Therefore, the area \( A_{\text{square}} \) of the square is: \[ A_{\text{square}} = (\text{side length})^2 = 20^2 = 400 \text{ square feet} \]
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Find the area of the circle: The area \( A_{\text{circle}} \) of the circle is given by the formula: \[ A_{\text{circle}} = \pi r^2 \] Substituting \( r = 10 \) feet and using \( \pi \approx 3.14 \): \[ A_{\text{circle}} = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square feet} \]
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Find the area of the shaded region: The area of the shaded region is given by the area of the square minus the area of the circle: \[ A_{\text{shaded}} = A_{\text{square}} - A_{\text{circle}} = 400 - 314 = 86 \text{ square feet} \]
Thus, the approximate area of the shaded region is \( \boxed{86} \) square feet.