Formulas wouldn't tell us squat if we couldn't turn around and apply them to situations in the real world. Fortunately, we can do just that. Formulas can help us figure out how to deal with, plan for, or manipulate objects of all different shapes and sizes, both two-dimensional and three-dimensional. The two-dimensional ones are easier, as you might imagine, so let's start there. This ain't a throw-you-in-the-deep-end-of-the-pool-to-teach-you-to-swim kind of lesson.
Two-dimensional shapes show up a lot in the world. A soccer field is a rectangle, the body of a bicycle may be a triangle, and some cakes have circular tops. These are all three-dimensional objects, but with two-dimensional parts. Practical considerations aside, two-dimensional shapes are good for math problems because we can draw them on paper. Because most paper that we know of is more or less 2D.
We'll run through some familiar shapes in the next few pages. For each shape, we'll give you a formula for the perimeter, meaning the distance around the outside of the shape, and a formula for the area, meaning the size of the surface covered by the shape. Perimeter is measured in units of length such as inches, feet, or miles. Area is measured in units of length squared, such as square inches, square feet, or square miles. Perimeter usually works better in poetry. For example, Robert Frost never would have been such a hit if he'd written that he had "square miles to go before I sleep."