To calculate the total surface area of a triangular prism, we will need the area of the triangular faces and the areas of the three rectangular faces. Since you mentioned that there is a figure but did not provide any dimensions, I will explain the steps to calculate each part.
1. Area of the Triangular Faces
Assuming the triangular face has a base \( b \) and height \( h \), the area \( A_t \) of one triangular face can be calculated using the formula:
\[ A_t = \frac{1}{2} \times b \times h \]
If there are two triangular faces (one on each end), the total area of both triangular faces would be:
\[ A_{triangles} = 2 \times A_t = 2 \times \left(\frac{1}{2} \times b \times h\right) = b \times h \]
2. Area of Rectangular Faces
Assuming the prism has three rectangular faces with lengths \( l_1, l_2, \) and \( l_3 \) corresponding to the sides of the triangular face, and common prism height \( H \):
- Area of the smallest rectangular face (adjacent to the smallest side \( l_1 \)):
\[ A_1 = l_1 \times H \]
- Area of the middle rectangular face (adjacent to the middle side \( l_2 \)):
\[ A_2 = l_2 \times H \]
- Area of the largest rectangular face (adjacent to the largest side \( l_3 \)):
\[ A_3 = l_3 \times H \]
3. Total Surface Area
The total surface area \( A_{total} \) of the triangular prism can be calculated as:
\[ A_{total} = A_{triangles} + A_1 + A_2 + A_3 \]
Substituting the areas calculated above:
\[ A_{total} = b \times h + (l_1 \times H) + (l_2 \times H) + (l_3 \times H) \]
Final Step
To provide you with the area calculations, I need specific values for \( b, h, l_1, l_2, l_3,\) and \( H \). If you have these dimensions, please provide them, and I can perform the calculations for you!