HMMT 1999 G8

Squares $A B K L, B C M N, C A O P$ are drawn externally on the sides of a triangle $A B C$. The line segments $K L, M N, O P$, when extended, form a triangle $A^{\prime} B^{\prime} C^{\prime}$. Find the area of $A^{\prime} B^{\prime} C^{\prime}$ if $A B C$ is an equilateral triangle of side length 2.