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Lesson 5: Surface area

# 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.

### 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.
\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.
\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.
\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.
\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.
unitssquared

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