Question 25
Four regular hexagons surround a square with a side length $1,$ each one sharing an edge with the square, as shown in the figure below. The area of the resulting $12$-sided outer nonconvex polygon can be written as $m\sqrt n + p,$ where $m,$ $n,$ and $p$ are integers and $n$ is not divisible by the square of any prime. What is $m + n + p?$
