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. Base 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 =7 
1/2 (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?