The surface area \( S \) of a triangular prism can be calculated using the formula:
\[ S = bh + (p \cdot h) + (2 \cdot A) \]
where:
- \( S \) = surface area of the triangular prism
- \( b \) = base length of the triangular base
- \( h \) = height of the prism (the length of the prism)
- \( p \) = perimeter of the triangular base (the sum of all sides of the triangle)
- \( A \) = area of the triangular base
Explanation of the Formula:
- \( A \) accounts for the area of the triangular base, and since there are two triangular bases in the prism, it is multiplied by 2.
- \( bh \) is the area of the three rectangular sides (the lateral surface area), which involves the base length \( b \) multiplied by the height \( h \) of the prism.
- \( p \cdot h \) represents the combined area of the three rectangular faces that connect the triangular bases, where \( p \) is the perimeter of the base and is multiplied by the height \( h \) of the prism.
Note:
To fully utilize the formula, you need to calculate the area \( A \) of the triangular base, which can be found using the specific formula for the area depending on whether you have the base and height or the lengths of the sides of the triangle (for example, using Heron's formula).