Surface Area of Prisms & Cylinders

Surface Area
(Prisms & Cylinders)

Area of Regular Polygons

Example: Find the Area

Example: Find the Area

Multiple Choice

In a regular polygon the line from the center to the mid-point of an outer side is a(n)

• Radius

• Central Angle

• Sine

• Apothem

Multiple Choice

Find the area of this regular polygon

• 81.8 m²

• 204.4 m²

• 408.8 m²

• 40.8 m²

Multiple Choice

Find the area.

• 12.75
• 191.25
• 19.125
• 95.625

Multiple Choice

Find the area of the shaded region.

• 13.5
• 54
• 67.5
• 13.5

Surface Area of Prisms

​Let's look at a few NETS of 3-D figures...

​Example: Finding the Surface Area of a Right Prism

​Step 1: Find the Apothem

​Step 3: Plug into the formula
SA = aP + Ph

​Step 2: Find the Perimeter of one of the bases.

​Example: Finding the Surface Area of a Right Prism

​Step 1: Find the Apothem

​Step 3: Plug into the formula
SA = aP + Ph

​Step 2: Find the Perimeter of one of the bases.

Multiple Choice

Find the lateral surface area of the shape shown? Use the left and right sides as the bases.

• 119.28 in²

• 102.48 in²

• 84 in²

• 101.76 in2

Multiple Choice

Find the lateral surface area of the figure shown.

• 672 cm²

• 480 cm²

• 576 cm²

• 864 cm²

Multiple Choice

Find the total surface area of the figure shown.

• 672 cm²

• 480 cm²

• 576 cm²

• 864 cm²

Surface Area of Cylinders

​Lateral Area = Circumference of the circle X height of cylinder!

​Important Formulas...

Find the Surface Area of the cylinder.

​Step 1: Find the Area of one base of the circle
(A = Πr²)
Multiply by 2 (two bases)

​Step 2: Find the Circumference of the circle
(C = 2Πr)
Multiply by the height

​Step 3: Add the Area of the bases and the Lateral Area
(2B + L) or (2Πr² + 2Πrh)

Find the Surface Area of the cylinder.

​Step 1: Find the Area of one base of the circle
(A = Πr²)
Multiply by 2 (two bases)

​Step 2: Find the Circumference of the circle
(C = 2Πr)
Multiply by the height

​Step 3: Add the Area of the bases and the Lateral Area
(2B + L) or (2Πr² + 2Πrh)

Multiple Choice

What is surface area?

• Inside of the object
• the sum of all the areas of all the shapes that cover the surface of the object.
• Something Coach G made up?
• Surface area is what you get when you boil unicorn tears. 

Multiple Choice

Find the Total Surface area of the cylinder. 

Use 3.14 for Π

• 62.8m
• 477.28 cm²
•  235.5 cm³
• 942 cm²

Multiple Choice

Find the total surface area of the figure. Don't forget to divide the diameter by 2 to find the radius. Round to the nearest tenth.

• 628.3 m²

• 1445.1 m²

• 1245 m²

• 816.8 m²

Class Assignment

Big Ideas Math

Complete: Surface Area of Prisms & Cylinders

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