To find the surface area of the triangular prism, we need to calculate the area of the two triangular bases and the three rectangular faces.
Step 1: Calculate the Area of the Triangular Base
The area of a triangle can be calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, the base of the triangle is 10 cm, and the height is 8 cm. Therefore, the area is: \[ \text{Area} = \frac{1}{2} \times 10 , \text{cm} \times 8 , \text{cm} = \frac{1}{2} \times 80 , \text{cm}^2 = 40 , \text{cm}^2 \]
Since there are two triangular bases, the total area of the triangular faces is: \[ \text{Total area of bases} = 2 \times 40 , \text{cm}^2 = 80 , \text{cm}^2 \]
Step 2: Calculate the Area of the Rectangular Faces
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Rectangular face 1: This face is adjacent to the base (10 cm) and the height of the prism (6 cm), so its area is: \[ \text{Area} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
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Rectangular face 2 (height side): The triangular prism height here is the side length of the triangle (10 cm) and the height of the prism (6 cm), so its area is: \[ \text{Area} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
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Rectangular face 3 (height side): This face also has its base as the base of the triangle (10 cm) and height (6 cm), therefore, its area remains: \[ \text{Area} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
The total area of the three rectangular faces is: \[ \text{Total area of rectangles} = 60 , \text{cm}^2 + 60 , \text{cm}^2 + 60 , \text{cm}^2 = 180 , \text{cm}^2 \]
Step 3: Calculate Total Surface Area
Now, we can sum the areas of the triangular bases and the rectangular faces to find the total surface area: \[ \text{Total Surface Area} = \text{Area of Bases} + \text{Area of Rectangles} \] \[ \text{Total Surface Area} = 80 , \text{cm}^2 + 180 , \text{cm}^2 = 260 , \text{cm}^2 \]
Therefore, the surface area of the triangular prism is: \[ \boxed{260 , \text{square centimeters}} \]