To find the surface area of a triangular prism, follow these steps:

1. Identify the dimensions:
   • Let the triangular base have sides S1,S2,S3S_1,S_2,S_3S1​,S2​,S3​.
   • Let the base have a height hhh and base length bbb (if the triangle is right-angled or height is known).
   • Let the length (or height) of the prism be LLL.
2. Calculate the area of the two triangular bases:
   • Use the formula for the area of a triangle:

Base Area=12×b×h\text{Base Area}=\frac{1}{2}\times b\times hBase Area=21​×b×h

 * Since there are two identical triangular bases, multiply by 2:

2×Base Area=b×h2\times \text{Base Area}=b\times h2×Base Area=b×h

3. Calculate the lateral surface area (the three rectangular faces):
   • Find the perimeter of the triangular base:

Perimeter=S1+S2+S3\text{Perimeter}=S_1+S_2+S_3Perimeter=S1​+S2​+S3​

 * Multiply the perimeter by the length of the prism:

Lateral Surface Area=Perimeter×L\text{Lateral Surface Area}=\text{Perimeter}\times LLateral Surface Area=Perimeter×L

4. Add the areas together for total surface area:

Surface Area=(Perimeter×L)+2×Base Area\text{Surface Area}=(\text{Perimeter}\times L)+2\times \text{Base Area}Surface Area=(Perimeter×L)+2×Base Area

Or explicitly:

Surface Area=(S1+S2+S3)×L+b×h\text{Surface Area}=(S_1+S_2+S_3)\times L+b\times hSurface Area=(S1​+S2​+S3​)×L+b×h

This formula accounts for the combined area of the two triangular bases and the three rectangular lateral faces

Summary formula:

Surface Area=(Perimeter of base×Length)+2×Base Area\boxed{ \text{Surface Area}=(\text{Perimeter of base}\times \text{Length})+2\times \text{Base Area} }Surface Area=(Perimeter of base×Length)+2×Base Area​

Additional notes:

• For a right triangular prism, if you know the two legs of the triangle, use 12×a×b\frac{1}{2}\times a\times b21​×a×b for the base area.
• If the triangle is not right-angled, use Heron's formula or trigonometric methods to find the base area.
• The lateral faces are rectangles whose widths correspond to the sides of the triangle and length is the prism's length

This method will give you the total surface area of any triangular prism.