NCERT Solutions for Class 9 Maths Unit 12
Heron's Formula Class 9
Unit 12 Heron's Formula Exercise 12.1, 12.2 Solutions
Introduction to Heron's Formula
Heron's formula for the area of a triangle with sides of length a, b, c is
A = sqrt(s (s-a) (s-b) (s-c))
where
s = (a+b+c)/2
It is unfortunate that this topic has essentially disappeared from school curriculum today. Calculation, given available calculations and computers, can no longer be a reason for avoiding the formula. In what follows, I hope to show some interesting and challenging problems using Heron's formula.
Whether or not one would pose the demonstration or proof of Heron's formula for a particular class would depend on the class. Initially, exploration with Heron's formula could involve computing areas using the formula and making comparison's of the results -- much as we pose analogous exercises in a meaningful way with the Pythagorean theorem long before a proof or demonstration is fully understood.