Solve for the surface area of the triangular prism.

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To solve for the surface area of a triangular prism, we need to know the dimensions of the base triangle and the height (or length) of the prism. The surface area \(S\) of a triangular prism can be calculated using the following formula:

\[ S = bh + l \cdot P \]

where:

  • \(b\) is the area of the triangular base,
  • \(h\) is the height (or length) of the prism,
  • \(l\) is the length of the prism,
  • \(P\) is the perimeter of the triangular base.
  1. Calculate the area of the triangular base: If the base triangle has a base \(a\) and height \(c\), the area \(A\) is given by: \[ A = \frac{1}{2} \times a \times c \]

  2. Calculate the perimeter of the triangular base: If the sides of the triangular base are \(a\), \(b\), and \(c\), the perimeter \(P\) is: \[ P = a + b + c \]

  3. Calculate the surface area: Combine the results in the surface area formula: \[ S = A \cdot h + l \cdot P \]

If you provide the specific dimensions (base and height of the triangle, and the height of the prism), I can help you calculate the surface area of the triangular prism.