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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, point, 5 rectangle.
Area of a rectangle=lengthwidth=41.5=6\begin{aligned} \text{Area of a rectangle} &= \text{length} \cdot \text{width}\\\\ &= 4 \cdot 1.5\\\\ &= {6} \\\\ \end{aligned}
The total area of both sides is 2, dot, 6, equals, start color #11accd, 12, end color #11accd.
The bottom and the top are both 4 by 5 rectangles.
Area of a rectangle=lengthwidth=45=20\begin{aligned} \text{Area of a rectangle} &= \text{length} \cdot \text{width}\\\\ &= 4 \cdot 5\\\\ &= {20} \\\\ \end{aligned}
The total area of bottom and the top is 2, dot, 20, equals, start color #1fab54, 40, end color #1fab54.
The back and the front are both 1, point, 5 by 5 rectangles.
Area of a rectangle=lengthwidth=1.55=7.5\begin{aligned} \text{Area of a rectangle} &= \text{length} \cdot \text{width}\\\\ &= 1.5 \cdot 5\\\\ &= {7.5} \\\\ \end{aligned}
The total area of the back and the front is 2, dot, 7, point, 5, equals, start color #e07d10, 15, end color #e07d10.
Let's add the areas to find the surface area.
Surface area=12+40+15=67\begin{aligned} \text{Surface area} &= \blueD{12}+ \greenD{40} + \goldD{15} \\\\ &= 67\\\\ \end{aligned}
The surface area of the rectangular prism is 67 unitssquared.

Practice set

Problem 1
  • Current
Find the surface area of the square pyramid shown below.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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

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