To calculate the surface area of the rectangular pyramid, we need to find the area of the base and the areas of the triangular faces.
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Base Area: The base of the pyramid 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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Side Areas: There are four triangular faces. We will calculate the area of each triangular face next.
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Triangle on longer side (10 ft):
- Base = 10 ft
- Height = 7 ft (slant height corresponding to the longer side) \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 , \text{ft} \times 7 , \text{ft} = 35 , \text{ft}^2 \]
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Triangle on shorter side (7 ft):
- Base = 7 ft
- Height = 8 ft (slant height corresponding to the shorter side) \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 , \text{ft} \times 8 , \text{ft} = 28 , \text{ft}^2 \]
Therefore, the surface area includes:
- Two triangles with 10 ft base area: \( 2 \times 35 , \text{ft}^2 = 70 , \text{ft}^2 \)
- Two triangles with 7 ft base area: \( 2 \times 28 , \text{ft}^2 = 56 , \text{ft}^2 \)
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Total Surface Area Calculation: \[ \text{Total Surface Area} = \text{Base Area} + \text{Side Areas} = 70 , \text{ft}^2 + 70 , \text{ft}^2 + 56 , \text{ft}^2 = 70 , \text{ft}^2 + 126 , \text{ft}^2 = 196 , \text{ft}^2 \]
Thus, the correct calculation for the surface area of the pyramid is: \[ \boxed{196 , \text{ft}^2} \]
So the correct response from the options is 196 ft² or 196 ft squared.