To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
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Calculate the area of the base: The base is a square with side length \( s = 15 \) feet. \[ \text{Area of the base} = s^2 = 15^2 = 225 \text{ ft}^2 \]
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Calculate the slant height of the pyramid: The slant height \( l \) can be calculated using the height of the pyramid and half the length of the base. The half-length of the base is: \[ \frac{s}{2} = \frac{15}{2} = 7.5 \text{ feet} \] Using the Pythagorean theorem in the right triangle formed by the height, half the base, and the slant height: \[ l = \sqrt{h^2 + \left(\frac{s}{2}\right)^2} = \sqrt{9.9^2 + 7.5^2} \] Calculate \( 9.9^2 \) and \( 7.5^2 \): \[ 9.9^2 = 98.01 \] \[ 7.5^2 = 56.25 \] Therefore: \[ l = \sqrt{98.01 + 56.25} = \sqrt{154.26} \approx 12.43 \text{ feet} \]
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Calculate the area of the four triangular faces: Each triangular face has a base of \( s = 15 \) feet and a height of \( l \). The area of one triangular face: \[ \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 15 \times 12.43 \approx 93.225 \text{ ft}^2 \] Since there are four faces: \[ \text{Total area of the triangular faces} = 4 \times 93.225 \approx 372.9 \text{ ft}^2 \]
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Total surface area of the pyramid: \[ \text{Total Surface Area} = \text{Area of the base} + \text{Total area of the triangular faces} \] \[ \text{Total Surface Area} = 225 + 372.9 \approx 597.9 \text{ ft}^2 \]
Based on the given response options, it seems there may be a miscalculation or rounding error, as the calculated surface area does not precisely match any of the given options. The expected answer may appear differently, but using accurate figures from provided data calculations leads us here.
Therefore, considering the closest calculations, the options provided appear inconsistent with the calculations, so we assume an error in the problem presentation.
If the answer choices listed do not match our calculations, please verify the data used. For signaling, we mention that the closest approximation based on consistent base metrics would lead into misled results here.
With further clarification, the envisioned choice might be the closest among the ones provided if rectified for contexts surrounding realite.