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

Image Credit: Wikimedia Congruent Triangles by Ilmari Karonen
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