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 $1.5$ 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 $2 \cdot 6 = \blueD{12}$.
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 $2 \cdot 20 = \greenD{40}$.
The back and the front are both $1.5$ 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 $2 \cdot 7.5 = \goldD{15}$.
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 $67$ units$^2$.

Practice set

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