# Triangle Area Sum 2

Geometry Level 5

Find all possible areas of a triangle with $$2$$ sides of lengths $$11$$ and $$12$$ and one angle $$60^{\circ}.$$

If the sum of the areas of the $$3$$ smallest triangles is $$a\sqrt{b},$$ where $$a$$ and $$b$$ are integers and $$b$$ is square-free, enter your answer as $$a+b$$.

This is part of the set Trevor's Ten.

Useful Brilliant Wikis - Triangles-Calculating Areas

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