Since your question is "conceptual" in nature, I will ask why would you want to calculate the Cpk? How do you intend on using this? Sorry, I will admit my bias is such metrics are not very useful. This due to the following reasons:
1. The enumerative statistics used in the calculation are estimates and how well they describe the true population is often in question (e.g., used a 30 piece sample without any explanation as to how the sample was obtained). When Cpk's are reported, they are reported as one number even though there is obviously a confidence interval around both of the statistics used in the metric.
2. When the Cpk does not meet your objective, you are left with disaggregating the metric to determine if it is a mean or variation problem. Why not just "track" those (mean, deviation from target and standard deviation, minimize)?
3. There is often misuse of Cpk's for comparison (e.g., comparing across different products)
4. How often is stability established before Cpk's are reported?
5. Specifications are often inappropriate.
see:
Gunter, Berton (1989) “The Use and Abuse of Cpk”, Quality Progress, January 1989
Can you please supply a real example of the situation you describe, where there is a specification (customer requirement) on the "area"?
If I understand the situation you describe, could you first understand the relationship between the 2 factors and the response variable (area), then, perhaps using tolerance parallelograms (see Shainin), understand the appropriate specs for each factor and use traditional Cpk for each factor independently?
"All models are wrong, some are useful" G.E.P. Box
