Two young mathematicians discuss the idea of area.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, I’ve have a troubling question.
Riley
Yes?
Devyn
What is area?
Riley
Oh, for a rectangle it is just
Devyn
Right. But shouldn’t it mean more?

Area is a funny thing. What is it really? Well the idea is this:

Define something as having a ‘‘unit’’ area, and see how many times it ‘‘covers’’ something.

The most obivious thing to use for our ‘‘unit’’ area is a unit square. From this we can quickly move on to find the area of any rectangle as

Sometimes area is described as ‘‘how much paint will cover a surface.’’ Is this accurate? What do you think?