## Surface Area of a Prism

**Common Core Standard: 7.G.6**

The surface area of a prism is total area of the surface of the prism. I like to visualize the surface area thinking how much material would it take to cover the object.

## Surface Area of Prism formula equals “P x h+2b “

P = Perimeter of the prism

h = height of the prism

b = base area

The formula for base area will vary according to the shape of the prism.

Here is a listing of **base area formulas**

## Surface Area of A Prism Problem

Find the surface area of a prism with a length of 3, a width of 4, and a height of 5.

__Option 1:__

Surface area formula = P x h + 2B

**Step 1**

**.**Find the perimeter length of the prism.

**Perimeter**= 3 + 4 + 3 + 4 = 14 units

**height**= 5 units

**Step 2.**

**Multiply**

**perimeter**times

**height**

14 x 5 = 70 sq. units

**Step 2.**

**Multiply**

**perimeter**times

**height**

14 x 5 = 70 sq. units

**Step 3.**B

**ase of the Prism**= 4 x 3 = 12

**Find the base area using length * width**

**Step 4.**2(12) = 24

**Now that you have the base area**

**multiply base area times two**

**Step 5.**Add

**step 2**and

**step 4**, this equals your surface area

70 + 24 = 94 sq. units squared

## Another option is to take the area of each side and add these together Option 2:

**Step 1**Find the

**area**of each side by multiplying

**Length times Width**

Area of the two end faces 4 X 3 = 12 * 2 = 24

Area of the top two faces 4 X 5 = 20 * 2 =40

Area of the two side faces 5 X 3 = 15 * 2 =30

**Step 2**. Add the area of each side together

24 + 40 + 30 = 94 units^2

Questions answered in this video….

How do you find the

**surface area of a rectangular prism**with side lengths of 5 and 4 units and a height of 5 units?What is the formula for surface area of a rectangle?

## Surface Area of A Prism Problem 2

Find the surface area of a

**hexagonal prism**with sides of 8 a height of 10 and an apothem of 7.The

**apothem**is the distance from the center of the base to the side of the base**Step 1**Find the base area using the formula

**1⁄2 a*p**

p=perimeter

a = apothem

**Perimeter**= 6 sides * 8 ( length of 1 side )= 48 unts

a =

**apothem**=71/2 (7 *48) = 168 units = perimeter of 1 base

168 * 2 = 336 will be the perimeter

( multiple by 2 because you have 2 bases)

**Step 2**Find the

**lateral Area**

**Lateral area = Perimeter of the Prism * Height**

Perimeter * Height = 48 * 10 = 480 units

**Step 3.**Add

**lateral area**+

**base area**

480 + 336= 816 units^2 =Surface Area of a Hexagonal Prism

## Watch this video to find the surface area of a hexagonal prism, but the apothem is not given.

Questions answered in this video…

How do find the surface area of a hexagonal prism?

How do you find the apothem of a prism?

What formula do you use to find the surface area of a hexagonal prism?

## Finding the surface area of a triangular prism

Follow these steps to find the surface area of a triangular prism

**Surface Area Triangular Prism**=Lateral Area + 2Base Areas

**Lateral Area**= Perimeter of the base x height

**Base area of a triangle**= 1/2 base x height

Find the surface area of the triangular prism on the left.

**Step 1.**Find the lateral area using Perimeter of base x height

16 + 12+ 20 = 48

48 x 10 = 480 cm^2

**Step 2**Find the base area using 1/2 base x height

1/2( 12 ) (16) = 96 cm^2

The reason that 12 is the base and 16 is the height is because

12 16 20 is a

**Pythagorean Triplet**( 3 4 5) As a result this is a right triangle, and the side of 12 units is the base and the side of 16 units becomes the height.If the

**height**is not given you can still find the base area using Heron’s Formula.Here is a video to show you how.

**Step 3.**Multiply base area from step 2 times two because you have one on each end.

96 x 2 = 192

**Step 4.**Add the lateral area from step 1., and the two base areas from step 3 for total surface area

480 + 192 = 672 cm^2

Questions answered with this video…

How do you find the surface area of a triangular prism?

What formula do you use for finding the surface area of a triangular prism?

Which side of the prism is the base?

What is lateral area?