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 44 by 1.51.5 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 26=122 \cdot 6 = \blueD{12}.
The bottom and the top are both 44 by 55 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 220=402 \cdot 20 = \greenD{40}.
The back and the front are both 1.51.5 by 55 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 27.5=152 \cdot 7.5 = \goldD{15}.
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 6767 units2^2.

Practice set

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