Who was Heron? And what is Heron’s formula?
Heron of Alexandria
Heron was born in about 10AD possibly in Alexandria in Egypt was an ancient Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition. He worked in applied mathematics. His works on mathematical and physical subjects are so numerous and varied that he is considered to be an encyclopedic writer in these fields. His geometrical works deal largely with problems on mensuration written in three books. Book I deals with the area of squares, rectangles, triangles, trapezoids (trapezia), various other specialized quadrilaterals, the regular polygons, circles, surfaces of cylinders, cones, spheres etc. In this book, Heron has derived the famous formula for the area of a triangle in terms of its three sides.
Heron’s Formula (Hero’s Formula)
According to Heron’s formula.
If there is a triangle with all its sides given.
For example: Let’s take a triangle with sides a, b and c
Half of perimeter of triangle (s) = a + b + c
Then, area(A) of triangle will be
Algebraic proof of Heron’s Formula
Here we have a figure,
In the above figure,
AB=c AC=b BC=a BD=h
CD=x and AD=b-x
Where is it used?
In the real life, we have many objects of the shape of a triangle. To find the surface area or the area of a triangular land, for example, we can use Heron’s formula. Also in real life the objects or lands are not always rectangular or regular shaped.
In real life we may not be able to draw perpendiculars from one vertex onto the base. Hence, the good way of finding the area is by measuring the sides on each side and then using Heron’s formula.