To find the surface area of the triangular prism, you need to calculate the area of the triangular base and the area of the three rectangular faces. Here's how to do it step by step:
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Calculate the area of the triangular base: The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base of the triangle is 10 cm, and the height is 8 cm.
\[ \text{Area} = \frac{1}{2} \times 10 , \text{cm} \times 8 , \text{cm} = \frac{1}{2} \times 80 = 40 , \text{cm}^2 \]
Since the prism has two triangular bases, the total area for the triangles is: \[ 2 \times 40 , \text{cm}^2 = 80 , \text{cm}^2 \]
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Calculate the area of the rectangular faces:
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There are three rectangular faces: two that connect to the base and one that connects between the triangular bases.
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Rectangle 1 (base side x height of prism): This rectangle has one side as the base of the triangle (10 cm) and a height corresponding to the length of the prism (6 cm). \[ \text{Area} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
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Rectangle 2 (side x height of prism): This rectangle connects to one of the triangle’s sides (10 cm) and also has a height of 6 cm. \[ \text{Area} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
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Rectangle 3 (other side x height of prism): This rectangle connects to the other triangle side (10 cm) again, corresponding to the same height. \[ \text{Area} = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2 \]
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Sum of the areas of the rectangular faces: \[ 60 , \text{cm}^2 + 60 , \text{cm}^2 + 60 , \text{cm}^2 = 180 , \text{cm}^2 \]
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Total Surface Area: Finally, sum the area of the triangular bases and the area of the rectangular faces: \[ \text{Total Surface Area} = 80 , \text{cm}^2 + 180 , \text{cm}^2 = 260 , \text{cm}^2 \]
Based on these calculations, the surface area of the triangular prism is 260 square centimeters.
Correct Response: 260 square centimeters.