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.
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
If the prism is regular, the bases are
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
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
In the figure above, click "hide details".
(To make it a little more challenging, hide the base area also.)
Drag the orange dots to set the shape of a new prism.