Finding Surface Area From a Net

You've already learned to unfold a solid into a netA two-dimensional pattern that can be folded up to form a three-dimensional figure., and you already know how to find the area of a flat shape. Put those two skills together and you can find surface areaThe total area of all the faces of a three-dimensional figure, found by adding up each face's area.: the total area covering the outside of a three-dimensional figure.

Here's the whole strategy in one sentence: lay the solid out as a net, find the area of every single face, then add all those areas together. There's no separate formula to memorize, because a net already shows you every face you need to measure. Some faces might repeat, like the two identical triangular bases on a triangular prism, so watch carefully so you don't skip a face or count one twice.

Surface area answers are always in square units, just like area, because you're still measuring flat space, just flat space wrapped around a solid instead of lying on a table. Once you can find the area of a net's faces accurately, surface area is really just careful addition.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.