The formula for the surface area \( S \) of a triangular prism can be expressed as:
\[ S = bh + l(a + b + c) \]
Where:
- \( S \) = surface area of the triangular prism
- \( b \) = length of the base of the triangular face
- \( h \) = height of the triangular face (the perpendicular distance from the base to the top vertex of the triangle)
- \( l \) = length of the prism (the distance between the two triangular faces)
- \( a \), \( b \), \( c \) = lengths of the sides of the triangular face
Explanation:
- Triangular Faces: The term \( bh \) represents the area of the triangular face of the prism.
- Rectangular Faces: The term \( l(a + b + c) \) accounts for the areas of the three rectangular faces that connect the corresponding sides of the triangular bases and extend the length \( l \) of the prism.
Thus, the surface area of a triangular prism is calculated by adding the area of the two triangular bases and the areas of the three rectangular sides.