Q:

How do I calculate width and height when increasing area of box

If I had a box 100px wide by 50px high, so the area is 500px squared.  what is the formula for calculating the new height and width of the container in pixels if I wanted to increase the overall area by 20% or 50% or whatever?  

A:

I'll assume you want to keep the width/height proportional. 
If you want to increase the area by 20% (multiplied by 1.20), multiply both the width and height by the square root of 1.20.