To find the surface area of the rectangular pyramid, we need to calculate the area of the base and the areas of the triangular faces.
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Base Area: The base is a rectangle with dimensions 10 ft and 7 ft.
\[ \text{Base Area} = \text{length} \times \text{width} = 10 , \text{ft} \times 7 , \text{ft} = 70 , \text{ft}^2 \]
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Lateral Surface Area: The pyramid has four triangular faces. We'll calculate the area of each triangular face separately.
- Triangular Face with Base 10 ft (using slant height 8 ft):
\[ \text{Area}_1 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 , \text{ft} \times 8 , \text{ft} = 40 , \text{ft}^2 \]
- Triangular Face with Base 7 ft (using slant height 7 ft):
\[ \text{Area}_2 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 , \text{ft} \times 7 , \text{ft} = 24.5 , \text{ft}^2 \]
Since there are two triangular faces with each base, we multiply each area by 2:
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For the face with base 10 ft: \[ 2 \times \text{Area}_1 = 2 \times 40 , \text{ft}^2 = 80 , \text{ft}^2 \]
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For the face with base 7 ft: \[ 2 \times \text{Area}_2 = 2 \times 24.5 , \text{ft}^2 = 49 , \text{ft}^2 \]
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Total Lateral Surface Area: \[ \text{Total Lateral Surface Area} = 80 , \text{ft}^2 + 49 , \text{ft}^2 = 129 , \text{ft}^2 \]
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Total Surface Area: \[ \text{Total Surface Area} = \text{Base Area} + \text{Total Lateral Surface Area} = 70 , \text{ft}^2 + 129 , \text{ft}^2 = 199 , \text{ft}^2 \]
Given the options presented, it appears there is a slight miscalculation in the values since the closest available option for the correct surface area is not listed distinctly among the choices: 126 ft², 70 ft², 196 ft², and 202 ft² do not match with 199 ft².
None of the choices perfectly match.
However, if we were to recalculate or have the option to round differently or if the set values were misrepresented, check if multiple interpretations of slant height can yield a different set of answers.
For clarity with the closest presented answer, the best focus towards a likely correct answer based on the options given would be "196 ft.²", as it might represent an estimate or simplification of the surface area calculation.