Equilateral \triangle A B C has side length 1 , and squares A B D E, B C H I, and C A F G lie outside the triangle. What is the area of hexagon D E F G H I ?

**Answer Choices**

A. \dfrac{12+3 \sqrt{3}}{4}

B. \dfrac{9}{2}

C. 3+\sqrt{3}

D. \dfrac{6+3 \sqrt{3}}{2}

E. 6