Let us say the sum of perimeter of square and circumference of circle be $L$

Given sum of the perimeters of a square and a circle.

Assuming, \[side\text{ }of\text{ }square\text{ }=\text{ }a\text{ }and\text{ }radius\text{ }of\text{ }circle\text{ }=\text{ }r\]

Then, \[L\text{ }=\text{ }4a\text{ }+\text{ }2\pi r\text{ }\Rightarrow \text{ }a\text{ }=\text{ }\left( L\text{}-\text{}2\pi r \right)/4\ldots \text{ }\left(1\right)\]

Let the sum of area of square and circle be $S$

So, \[S\text{ }=\text{ }{{a}^{2}}~+\text{ }\pi {{r}^{2}}\]