What's the Area? (Part I)

This is the first of a series of posts titled What's the Area? These posts will discuss various means of finding the area of the blue trapezoid in the following figure.



This isn't a difficult problem, and I'm going to discuss things in the simplest terms I can muster.

I don't hope to produce an exhaustive list of means of finding the area in question--just a progression of means to serve as a basis for discussion. Comments are encouraged.

To avoid confusion, let's define the problem a little more explicitly...

The blue trapezoid above is enclosed in a unit square (1 x 1). The height of its left side is 0.4 and the height of its right size is 0.7.

What's the Area?

In the next post, we'll look to geometry for a solution.