2004 #02 and 40

A nice fraction and a seemingly simply area question. Nice!

Difficulty: Simple.

Difficulty: Easy after the AHA! moments. 

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 02, answer 40.