NCERT Book Class 9 Maths Chapter 10 Heron's Formula

CHAPTER 10

HERON’S FORMULA

10.1 Area of a Triangle — by Heron’s Formula
1
We know that the area of triangle when its height is given, is × base × height. Now
2
suppose that we know the lengths of the sides of a scalene triangle and not the height.
Can you still find its area? For instance, you have a triangular park whose sides are 40
m, 32 m, and 24 m. How will you calculate its area? Definitely if you want to apply the
formula, you will have to calculate its height. But we do not have a clue to calculate
the height. Try doing so. If you are not able to get it, then go to the next section.
Heron was born in about 10AD possibly in Alexandria in
Egypt. 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 specialised
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 Heron (10 C.E. – 75 C.E.)
terms of its three sides. Fig. 10.1

The formula given by Heron about the area of a triangle, is also known as Hero’s
formula. It is stated as:

Area of a triangle = s( s − a ) ( s − b ) ( s − c ) (I)