Definition: Surface area is the total area of all the faces of a three-dimensional figure, measured in square units.
What is surface area?
It is the amount of material needed to cover the outside of a solid, such as the paper to wrap a gift box. Add up the areas of every face.
How do you find it for a prism?
Unfold the solid into a net, then add the areas of the rectangles and other polygons. For a box 8 cm long, 5 cm wide, and 3 cm tall:
- Top and bottom: 2 x (8 x 5) = 80
- Front and back: 2 x (8 x 3) = 48
- Left and right: 2 x (5 x 3) = 30
Total: 80 + 48 + 30 = 158 square centimeters.
What about a pyramid?
A square pyramid has a square base and four triangles. Find the base area and add the four triangle areas.
How is it different from volume?
Surface area counts square units on the outside. Volume counts cubic units inside. A box can have a large surface area and a small volume if it is thin.
What is the common error?
Missing a face. Count the faces before you add: a rectangular prism has six.
Where to learn it
- Unfolding Solids: Nets and Surface Area – lesson
- Prisms: Surface Area, Volume and Composite Figures – lesson