To find the surface area of a triangular pyramid, you need to calculate the area of the base and the area of the three triangular faces and then sum them together.
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Area of the base (which is a triangle):
- The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
- Given the base of the triangle is 10 and the height is 8.7: \[ \text{Area}_{\text{base}} = \frac{1}{2} \times 10 \times 8.7 = 43.5 \]
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Area of the triangular faces:
- Each triangular face has a base equal to the side of the base triangle (which is 10) and a height equal to the slant height (12). There are three triangular faces.
- The area of one triangular face would be: \[ \text{Area}_{\text{face}} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 12 = 60 \]
- Since there are three faces, the total area of the triangular faces is: \[ \text{Total Area}_{\text{faces}} = 3 \times 60 = 180 \]
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Total Surface Area:
- Now, sum the area of the base and the total area of the triangular faces: \[ \text{Total Surface Area} = \text{Area}{\text{base}} + \text{Total Area}{\text{faces}} = 43.5 + 180 = 223.5 \]
Therefore, the surface area of the triangular pyramid is 223.5.
So, the correct response is: 223.5.
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