Brunn-Minkowski Inequality : A Partucular Example of a 2 dimensional set.

Question

I have an inequality - $(R_{C+D})^{2} \geqslant (R_{C})^{2} + (R_{D})^{2}$. Representing it as $((R_{C+D})^{4})^{1/2} \geqslant ((R_{C})^{4})^{1/2} + ((R_{D})^{4})^{1/2}$, it follows from Brunn-Minkowski inequality relating two sets, C and D with their volumes that these sets exist in a 2-dimensional space with some addition operation between its elements, where volume of the set goes to $vol(C) \propto (R_{C})^{4} $ where $R_{C}$ represents some parameter representing set C. Elements of set C are functions of $R_{C}$ along with some other parameter, if required.
I was wondering if there is any particular example of a 2-dimensional set or if there is any procedure to construct or if there exists some representation of it. And also what is the addition operation defined on such set. Thanks.