how can we derive Heron's formula

To derive Heron's formula, draw a perpendicular from any vertex to opposite side in a given triangle, so that we get two right angled triangles.

The area of the given triangle is the addition of areas of these two right angled triangles, 

The height and base in any one triangle are the only variables, and we can connect them by Pythagorus's theorem.

The we would like to eliminate the the two variables height and base, from this area expression, and as we go to do that, we'll get Heron's formula.

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TopperLearning.