To find the surface area of a rectangular pyramid, we need to calculate the area of both the base and the triangular faces (lateral surface area).
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Base Area: Since the base is a rectangle with side lengths of 8 and 10: \[ \text{Base Area} = \text{length} \times \text{width} = 8 \times 10 = 80 \]
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Lateral Surface Area: The lateral surface area consists of the areas of the four triangular sides. We need to calculate the area of each triangle. The two slant heights correspond to the two different lengths of the base.
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For the triangular faces corresponding to the length of 10 (with slant height 12):
- Area of one triangle: \[ \text{Area}_1 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 12 = 60 \]
- Since there are two such triangular faces: \[ \text{Total Area for first pair} = 2 \times 60 = 120 \]
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For the triangular faces corresponding to the length of 8 (with slant height 15):
- Area of one triangle: \[ \text{Area}_2 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 15 = 60 \]
- Since there are two such triangular faces: \[ \text{Total Area for second pair} = 2 \times 60 = 120 \]
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Total Lateral Surface Area: Now add the areas of the triangular faces: \[ \text{Total Lateral Surface Area} = 120 + 120 = 240 \]
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Total Surface Area: Finally, we add the base area to the total lateral surface area: \[ \text{Total Surface Area} = \text{Base Area} + \text{Total Lateral Surface Area} = 80 + 240 = 320 \]
Therefore, the total surface area of the rectangular pyramid is \( \boxed{320} \).