To calculate the surface area of a triangular prism, you typically decompose it into its constituent faces. A triangular prism consists of two triangular bases and three rectangular lateral faces. The formula for its surface area involves the area of the two triangles and the area of the three rectangles.
Given the options:
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Decomposing the triangular prism into three triangles and two rectangles is not valid because there are only two triangular bases.
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The response that indicates finding the sum of three times the area of one triangle and twice the area of one rectangle is also not valid.
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The option stating to decompose into two triangles and three rectangles is valid, but finding just the sum of the area of one triangle and three times the area of one rectangle is incorrect; you need to account for both triangles and the total area of rectangles appropriately.
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The repeated options of decomposing into two triangles and three rectangles, along with adding up the area of all the shapes, best describes a valid method.
Thus, the correct phrasing that describes a valid method is:
"Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of both triangles and the area of all three rectangles."
It's important to sum the areas of both the triangles and the rectangles to get the total surface area.