To calculate the surface area of a triangular prism, we need to know the area of the triangular base and the area of the three rectangular faces.
Let's assume:
- Base (b) of the triangle = 8 cm
- Height (h) of the triangle = 6 cm
- Length (l) of the prism = 10 cm
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Area of the triangular base: \[ \text{Area}{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 , \text{cm}^2 \] Since there are two triangular bases, the total area for the triangular bases is: \[ \text{Total Area}{\text{triangles}} = 2 \times 24 = 48 , \text{cm}^2 \]
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Area of the rectangular faces:
- The first rectangle (base * length): \[ \text{Area}_{\text{rect1}} = 8 \times 10 = 80 , \text{cm}^2 \]
- The second rectangle (height * length): \[ \text{Area}_{\text{rect2}} = 6 \times 10 = 60 , \text{cm}^2 \]
- The third rectangle involves the side of the triangle. To find the side of the triangle (assuming it is a right triangle), we can calculate the hypotenuse (c): \[ c = \sqrt{(8^2 + 6^2)} = \sqrt{(64 + 36)} = \sqrt{100} = 10 , \text{cm} \] Then, \[ \text{Area}_{\text{rect3}} = 10 \times 10 = 100 , \text{cm}^2 \]
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Total surface area: \[ \text{Total Surface Area} = \text{Total Area}{\text{triangles}} + \text{Area}{\text{rect1}} + \text{Area}{\text{rect2}} + \text{Area}{\text{rect3}} \] \[ \text{Total Surface Area} = 48 + 80 + 60 + 100 = 288 , \text{cm}^2 \]
Therefore, the surface area of the triangular prism is 288 square centimeters.