To find the surface area of the triangular prism, we need to calculate the areas of all the individual faces and then sum them up.
Base: The base is a triangle with base 12.5 cm and height 11.5 cm, so its area is (1/2) * base * height = (1/2) * 12.5 * 11.5 = 71.875 cm^2
Front and back faces: These are rectangular faces with dimensions 10 cm by 11.5 cm, so each face has an area of 10 * 11.5 = 115 cm^2. Since there are two of these faces, the total area is 2 * 115 = 230 cm^2
Side faces: These are trapezoidal faces with bases 10 cm and 12.5 cm, and height 4 cm. The area of each trapezoidal face is given by (1/2) * (base1 + base2) * height = (1/2) * (10 + 12.5) * 4 = 45 cm^2. Since there are two of these faces, the total area is 2 * 45 = 90 cm^2
Now, summing up all the individual areas:
Base + Front and back faces + 2 * Side faces = 71.875 + 230 + 90 = 391.875 cm^2
Therefore, the surface area of the triangular prism is 391.875 cm^2, which needs to be rounded to two decimal places, resulting in 391.88 cm^2.
Correct answer: 391.88 cm^2
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