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Surface area review

Review surface area and try some practice problems.

What is surface area?

Surface area is the amount of space covering the outside of a three-dimensional shape.

Finding surface area

To calculate surface area, we add the areas of all the faces of the three-dimensional figure.
Want to learn more about finding surface area? Check out this video.

Example: Rectangular prism

Find the surface area of the right rectangular prism shown below.
Let's draw a net of the rectangular prism.
Each of the sides is a 4 by 1.5 rectangle.
Area of a rectangle=lengthwidth=41.5=6
The total area of both sides is 26=12.
The bottom and the top are both 4 by 5 rectangles.
Area of a rectangle=lengthwidth=45=20
The total area of bottom and the top is 220=40.
The back and the front are both 1.5 by 5 rectangles.
Area of a rectangle=lengthwidth=1.55=7.5
The total area of the back and the front is 27.5=15.
Let's add the areas to find the surface area.
Surface area=12+40+15=67
The surface area of the rectangular prism is 67 units2.

Practice set

Problem 1
Find the surface area of the square pyramid shown below.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Want to try some more surface area problems? Check out this exercise.

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