Area of a triangle using determinants of side lengths (not coordinates of vertices)

Mathematics Asked by rohitt on November 12, 2020

Given the side lengths of a triangle (and not the coordinates of vertices) is there a way to find the area of a triangle using determinants?

For example, if the three side lengths are $a$, $b$, and $c$ then the area could be easily found by the Heron’s formula. $A = sqrt{s(s-a)(s-b)(s-c)}$ where $s= frac{a+b+c}{2}$

Is there a way to find the area of this triangle using determinants?

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