Geometry · Triangle area · Regular hexagon · Law of cosines · Dissection
In a triangle \(ABC\) the angle at \(A\) measures \(60^\circ\). Write \(a\), \(b\), \(c\) for the lengths of the sides \(BC\), \(CA\), \(AB\). Prove that the area of the triangle equals
\[ \frac{\sqrt{3}}{4}\left(a^2 - (b-c)^2\right) . \]
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Serbian Regional Competition (Okruzno takmicenje) 2000, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source