# Surface Area of a Triangular Prism

Sub Topics
A Prism is a three dimensional polyhedron with two parallel faces called bases and lateral faces which are rectangles. The base of the Prism determines the name of the prism.

If the base is a triangle, then the prism is triangular. If the base is a square, then the prism is square and so on.

## Triangular Prism

If the base of the prism is triangular in shape, then the prism is called triangular prism.
A triangular prism has 3 lateral faces and 2 base. The bases are triangular in shape and lateral faces are rectangular. It has 6 vertices and 9 vertices.

## Formula for Surface Area of a Triangular Prism

The total area on the outer part of a prism is called total surface area. Total surface area constitute the lateral surface area and the two base areas.

The area of the lateral faces of the triangular prism is called Lateral surface area and the area of the base is called the Base area.
The formula for the total surface area of a Triangular prism is
Total Surface area = 2 x Base area + Lateral surface area

= 2 x ½ x b x h + h(s1 + s2 + s3)
= ba + h(s1 + s2 + s3)
where b is the base edge, a is the altitude of the base, h is the height of the prism, s1, s2, s3 are the sides of the triangle.

If the base is a scalene triangle and the base edges are a, b and c.  Then
Base area Δ = √s(s-a)(s-b)(s-c) where s = $\frac{(a + b + c)}{2}$

If the base is a scalene triangle and the base edges are a, b and c.  Then
Base area Δ = $\frac{\sqrt{3a^2}}{4}$ where a is the edge of the base.

## How to find the Surface Area of a Triangular Prism

The surface area of a triangular prism includes the lateral surface area and the base areas. To find the lateral surface area, we find the base perimeter by adding the base edges and then multiply it by the height of triangular prism.

To find the base area, we use the formulas based on the triangle at the base.

If the base is a scalene triangle, the we use the formula √s(s-a)(s-b)(s-c) where s = $\frac{(a + b + c)}{2}$ to find the base area. Similarly if the base is an equilateral triangle, then we use the formula $\frac{\sqrt{3a^2}}{4}$ to find the base area and then multiply be height.

After finding the base areas and lateral surface area, we just have to add them to get the total surface area.

## Calculating Surface Area of a Triangular Prism

Lets consider a few examples on triangular prism.