how can we derive heron's formula?

We can derive the Heron's formula, by following steps.

1/ The area of a given triangle is (base)(height)/2.

2/So we select a base as one of the side and draw a perpendicular to it, the height.

3/As we can see the triangle is now divided into two right angled triangles, we can obtain expression for base and height using Pythagorus's formula.

4/We substitute the newly obtained base and height expression into the area expression, and do little algebra to finally get the Heron's formula.

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Team,

TopperLearning.