To find the surface area of the triangular prism, we need to calculate the area of the triangular bases and the areas of the rectangular sides.
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Area of the triangular base: The triangle is equilateral with all sides measuring 10 cm. We can use the formula for the area of the triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
The base is 10 cm and the height is given as 8 cm, so:
\[ \text{Area} = \frac{1}{2} \times 10 \times 8 = 40 \text{ square centimeters} \]
Since there are two triangular bases:
\[ \text{Total area of triangular bases} = 2 \times 40 = 80 \text{ square centimeters} \]
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Area of the rectangular faces: There are three rectangular faces to consider. The measurements are as follows:
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Two rectangles that correspond to the sides of the prism that connect the triangle to the rectangular base have a width of 6 cm (the length of the prism) and heights equal to the side of the triangle (10 cm):
- Area of each of these rectangles: \[ \text{Area} = \text{width} \times \text{height} = 6 \times 10 = 60 \text{ square centimeters} \]
- Total for both rectangles: \[ 2 \times 60 = 120 \text{ square centimeters} \]
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One rectangle that corresponds to the bottom of the prism which has a width of 6 cm (the length of the prism) and a length of 10 cm (the base of the triangle):
- Area of this rectangle: \[ \text{Area} = 6 \times 10 = 60 \text{ square centimeters} \]
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Total surface area: Sum the areas we calculated: \[ \text{Total Surface Area} = \text{Area of triangular bases} + \text{Area of rectangular faces} \]
\[ = 80 + 120 + 60 = 260 \text{ square centimeters} \]
Thus, the surface area of the triangular prism is 260 square centimeters.