To find the surface area of the triangular prism, we need to calculate the area of the triangular base and the area of the three rectangular faces.
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Area of the triangular base: The formula for the area of a triangle is given by: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base of the triangle is 10 cm and the height is 8 cm. Thus, the area of the triangular base (A_triangle) is: \[ A_{\text{triangle}} = \frac{1}{2} \times 10 \times 8 = 40 \text{ square centimeters} \]
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Total area of the two triangular bases: Since there are two triangular bases in the prism: \[ A_{\text{two triangles}} = 2 \times 40 = 80 \text{ square centimeters} \]
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Area of the rectangular faces: The prism has three rectangular faces. The dimensions of these are:
- Two rectangles corresponding to the sides of the triangle (both 10 cm by the height of the prism, which is 6 cm): \[ A_{\text{rect 1}} = 10 \times 6 = 60 \text{ square centimeters} \] There are two of these rectangles: \[ A_{\text{two rects}} = 2 \times 60 = 120 \text{ square centimeters} \]
- One rectangle corresponding to the base of the triangle: \[ A_{\text{rect 2}} = \text{base} \times \text{height of prism} = 10 \times 6 = 60 \text{ square centimeters} \]
Therefore: \[ A_{\text{rectangles}} = 120 + 60 = 180 \text{ square centimeters} \]
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Total surface area of the prism: \[ A_{\text{total}} = A_{\text{two triangles}} + A_{\text{rectangles}} = 80 + 180 = 260 \text{ square centimeters} \]
Thus, the surface area of the triangular prism is 260 square centimeters.
The answer is: 260 square centimeters.