Surface Area of a Right Prism

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 parallel polygon bases and lateral faces that are adjacent to both bases.

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.

A right prism is a prism
whose lateral faces are all rectangles
and are perpendicular to the bases.

Formula

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

A = 2B + Ph

A: Surface area of a right prism
B: Base area
P: Perimeter of the base
h: height of the prism

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

Example 1

Find the surface area of the given right prism. Edges: 8, 7, 3.

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

Find the surface area of the given right prism. Edges: 4, 7.

Set the front face as the base.

The base is an equilateral triangle.
Its sides are all 4.

So B = (√3/4)⋅42.

Area of an equilateral triangle

Cancel the denominator 4
and reduce 42 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.