Triangle/Area from side lengths/Exercise

Let ${}a,b,c$ be the side lengths of a triangle. Show that the area of the triangle equals

${}F={\frac {\sqrt {2a^{2}c^{2}+2c^{2}b^{2}+2a^{2}b^{2}-a^{4}-b^{4}-c^{4}}}{4}}\,.$

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