How to find the surface area of triangular prisms?

Steps to Solve

1. Calculate the area of one triangular base

The area of a triangle is calculated by using the formula:

$$ A_{triangle} = \frac{1}{2} \times base \times height $$

2. Calculate the total area of the two triangular bases

Multiply the area of one triangular base by 2.

$$ A_{two_triangles} = 2 \times A_{triangle} $$

3. Calculate the area of each rectangular face

Each rectangular face is calculated by multiplying the length of the prism by a side of the triangle (base or slant height of the triangle). If the triangle has sides $a$, $b$, and $c$, then the areas of the rectangular faces are:

$$ A_{rect1} = length \times a $$

$$ A_{rect2} = length \times b $$

$$ A_{rect3} = length \times c $$

4. Sum the areas of the rectangular faces

Add the areas of all three rectangular faces together:

$$ A_{rect}_total = A_{rect1} + A_{rect2} + A_{rect3} $$

5. Add the areas of the triangular bases and rectangular faces

The total surface area of the triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces:

$$ A_{total} = A_{two_triangles} + A_{rect}_total $$