Math CentralQuandaries & Queries


Question from nick:

why is the area of a square of a given circumference greater than the area of a rectangle with the same circumference ?

We usually call the distance around the edge of a polygon a "perimeter," but I know what you mean.

Anyhow, there are lots of ways of thinking about it. Suppose the square has all four edges A and the rectangle has two opposite edges A+B. What are the other two edges of the rectangle?

What is the are of the square? Of the rectangle?

What is the area of the square minus the area of the rectangle?

Why is the square bigger than the rectangle?

Good Hunting!

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