Area of Copper Needed to dissipate 24 W
I don't think you have a hope of getting there. Here is a good reference, I'll post the graph from the end of their exercise. Note that you are asking for 2.5°C/W (not sure if that's including thermal resistance from junction to board or not, but let's assume that it's case temperature you are specifying). 



Note that increasing the area from 75mm x 75mm to 100mm x 100mm (77% increase in area) only slightly decreases the thermal resistance, from about 50°C/W to maybe 40°C/W. 

It's not simple linear equations to calculate this kind of thing- finite element modelling or building a mockup is going to give the best results, but I think we can conclude that anything much better than about 20-25°C/W is unlikely. 

Here's what a suitable commercial heat sink looks like. It's about 3" x 4.125" x 1" (76mm x 95mm x 25.4mm) and the aluminum is 4.7mm thick at the base.