# A problem by minimario minimario

Level pending

The following picture shows a portion of the New Year's Day decorations on the street, as the communities welcome $$2014$$. The decorations comprise of an equilateral triangle, colored yellow, and a square, colored green, which share vertex B. When measured, the distance from vertex $$E$$ to the ground $$(EH)$$ is $$8$$ miles, while the distance from vertex $$C$$ to the ground $$(CG)$$ is $$2+\sqrt{3}$$ miles. Additionally, the flags are joined such that $$\angle FBC=120^\circ$$.

Let the sum of the three areas (not decorated by flags) $$ACG, BAD,$$ and $$HED$$ be $$k$$ $$\text{mi}^2$$. Find $$\lceil k \rceil$$.

Note:$$\lceil x \rceil$$ denotes the least integer greater than or equal to $$x$$.

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