NAME:
Teaching Point: SWBAT describe and find the surface area of prisms using a formula
Essential Questions
How can you find the surface area of a prism using a formula?
Vocabulary
The surface area of a prism is the sum of the areas of all its faces.
Today, we will use a formula to find the surface area. The general formula for surface area of a prism is:
𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = 𝑷𝑯 + 𝟐𝑩
𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 (𝒊𝒏 𝒘𝒐𝒓𝒅𝒔) = (𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝐵𝑎𝑠𝑒)(𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝐹𝑎𝑐𝑒) + 2 (𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝐵𝑎𝑠𝑒)
EXAMPLE 1
Find the surface area.
a.) How many bases do you have on this prism?
b.) What shape is the base? What formula would you use to find
the area of the base?
c.) What is the height of the lateral face?
Perimeter of the Base
Area of the Base
𝑙=
𝑤=
ℎ=
EXAMPLE 2
Find the surface area of the triangular prism.
b.) How many bases do you have on this prism?
b.) What shape is the base? What formula would you use to find
the area of the base?
c.) What is the height of the lateral face?
Perimeter of the Base
Area of the Base
GUIDED PRACTICE
Directions: Find the surface area of each prism. Solve the problems in the manner of the examples.
GP1)
GP2)
GP3)
GP4)
GP5) Name a real-life situation where you might want to find the surface area of a prism.
INDEPENDENT PRACTICE
Directions: Find the surface area of each prism. Solve the problems in the manner of the examples.
1)
2)
3)
4)
5) A gift box is being wrapped. The box is 8 inches
by 8 inches by 10 inches. What is the least
amount of wrapping paper needed to wrap the
gift box?
6) The prism has a surface area of 392 cm2.
Find the height, x, of the prism.
8) A student found a shortcut. The student said the lateral surface area can be found by finding the
perimeter of the base and multiplying this by the height of the prism. Why does this work? Use
problems 1 & 4 from above to help explain your answer.
8) A company is deciding on the dimensions of a new storage box. Both boxes have a volume of 480
cubic inches, but the shapes are different. The table below shows the dimensions of both boxes.
Box 1
Box 2
Length
20 in.
15 in.
Width
6 in.
4 in.
Height
4 in.
8 in.
The material to make each box is $1.25 per square foot.
A) Which box is cheapest to produce? Explain your answer.
B) How much does a company save by choosing to make 50 of the cheaper box compared to 50 of
the more expensive box? Explain your answer.