I have a rectangle with sides "a" (width) and "b" (length).

If I find the midpoint of "b" and draw a line from it to a corner ("c"), it forms a triangle with the sides a, b/2 and c.

It is a right-angle triangle with c being the hypotenuse.

Therefore a^2+(b/2)^2=c^2

What is the relationship between side "c" and the area of the rectangle (ab)?