Surface area of a right prism

b= area of a base
p= perimeter of a base
h= height of the prism

Try this Change the height and dimensions of the triangular prism by dragging the orange dots. Note how the surface area is calculated.

A right prism is composed of a set of flat surfaces.

The two base are congruent polygons.
The lateral faces (or sides) are rectangles.

The total surface area is the sum of these.

Bases

Each base is a polygon. In the figure above it is a regular pentagon, but it can be any regular or irregular polygon. To find the area of the base polygons, see Area of a regular polygon and Area of an irregular polygon. Since there are two bases, this is doubled and accounts for the "2b" term in the equation above.

Lateral faces

Each lateral face (side) of a right prism is a rectangle. One side is the height of the prism, the other the length of that side of the base.

Therefore, the front left face of the prism above is its height times width or

The total area of the faces is therefore

If we factor out the 'h' term from the expression we get

Note that the expression in the parentheses is the perimeter (p) of the base, hence we can write the final area formula as

Regular prisms

If the prism is regular, the bases are regular polygons. and so the perimeter is 'ns' where s is the side length and n is the number of sides. In this case the surface area formula simplifies to

b= area of a base
n= number of sides of a base
s= length of sides of a base
h= height of the prism

Oblique prisms

There is no easy way to calculate the surface area of an oblique prism in general. The best way is to work from the fact that it is composed of two bases whose areas can be calculated as above. But to find the areas of the faces, you would need to consider them separately and find the area of each based on what you are given.

Things to try