To find the area of the shaded region, we first need to calculate the area of the square and then subtract the area of the circle that is cut out.
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Calculate the area of the square: The diameter of the circle is 10 feet, so the length of one side of the square is also 10 feet (since the circle touches all four sides of the square).
The area of the square \( A_{square} \) is given by the formula: \[ A_{square} = \text{side}^2 \] Substituting the side length: \[ A_{square} = 10^2 = 100 \text{ square feet} \]
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Calculate the area of the circle: The radius \( r \) of the circle is half of the diameter: \[ r = \frac{10}{2} = 5 \text{ feet} \] The area of the circle \( A_{circle} \) is given by the formula: \[ A_{circle} = \pi r^2 \] Using \( \pi \approx 3.14 \): \[ A_{circle} = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ square feet} \]
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Calculate the area of the shaded region: The area of the shaded region \( A_{shaded} \) is the area of the square minus the area of the circle: \[ A_{shaded} = A_{square} - A_{circle} \] Substituting the areas we calculated: \[ A_{shaded} = 100 - 78.5 = 21.5 \text{ square feet} \]
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Round to the nearest square foot: Rounding \( 21.5 \) square feet to the nearest whole number gives us: \[ A_{shaded} \approx 22 \text{ square feet} \]
Therefore, the area of the shaded region is approximately 22 square feet.
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