Formulas wouldn't tell us squat if we couldn't then 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 may imagine—let's start there. We're not a throw-you-in-the-deep-end-of-the-pool-to-teach-you-to-swim kind of people.
Two-dimensional shapes appear 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 two-dimensional.
We will go through some familiar shapes in the next few pages. For each shape we will 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."