# Surface Area of a Right Prism

How to find the surface area of a right prism: definition, formula, examples, and their solutions.

## Prism

A prism is a 3D figure

that has

a pair of polygon [bases] (brown)

and [lateral faces]

which are adjacent to both bases.

The [bases] are congruent and parallel.

The [lateral faces] are the faces

that are not the bases.

## Right Prism

A right prism is a prism

whose lateral faces are all rectangles

and are perpendicular to the bases.

## Formula

*A* = 2*B* + *Ph**A*: Surface area of a right prism*B*: Base area*P*: Perimeter of the base*h*: height of the prism

2*B*: Sum of the base areas*Ph*: Lateral area

## Example 1

Set the bottom face as the base.

The base is a rectangle.

Its sides are 7 and 5.

So *B* = 35.

Area of a rectangle

The sides of the base are 7 and 5.

And there are two pairs of 7 and 5.

So the perimeter of the base is*P* = (7 + 5)⋅2.

7 + 5 = 12

12⋅2 = 24

So *P* = 24.

It says

the given figure is a right prism.

So *h* = 8.

*B* = 35*P* = 24*h* = 8

So *A* = 2⋅35 + 24⋅8.

2⋅35 = 70

24⋅8 = 192

70 + 192 = 262

So *A* = 262.

## Example 2

Set the front face as the base.

The base is an equilateral triangle.

Its sides are all 4.

So *B* = (√3/4)⋅4^{2}.

Area of an equilateral triangle

Cancel the denominator 4

and reduce 4^{2} to 4.

Then *B* = 4√3.

The sides of the base are all 4.

And there are three congruent sides.

So the perimeter of the base is*P* = 4⋅3.

4⋅3 = 12

So *P* = 12.

It says

the given figure is a right prism.

So *h* = 7.

*B* = 4√3*P* = 12*h* = 7

So *A* = 2⋅4√3 + 12⋅7.

2⋅4√3 = 8√3

12⋅7 = 84

Arrange the terms.

Write the radical term (8√3)

behind the non-radical term (84).

So *A* = 84 + 8√3.