Find the total surface area of the triangular prism.

Sure, let's find the total surface area of the triangular prism step by step.

1. Identify the dimensions of the triangular prism:

   • The base of the triangular face (b)
   • The height of the triangular face (h)
   • The length of the prism (l)
   • The sides of the triangular face (a, b, c)

2. Calculate the area of the triangular base: The area of a triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times b \times h$

3. Calculate the area of the three rectangular faces:

   • The area of the rectangle with base $a$ and length $l$: $\text{Area of rectangle 1} = a \times l$
   • The area of the rectangle with base $b$ and length $l$: $\text{Area of rectangle 2} = b \times l$
   • The area of the rectangle with base $c$ and length $l$: $\text{Area of rectangle 3} = c \times l$

4. Calculate the total surface area: The total surface area of the triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces: $\text{Total surface area} = 2 \times \left(\frac{1}{2} \times b \times h\right) + (a \times l) + (b \times l) + (c \times l)$ Simplify the expression: $\text{Total surface area} = b \times h + a \times l + b \times l + c \times l$

So, the total surface area of the triangular prism is: $\text{Total surface area} = b \times h + l \times (a + b + c)$

Make sure to plug in the specific values for $a$, $b$, $c$, $h$, and $l$ to get the numerical answer.