This chapter deals with the area of a triangle when all the sides of it are given. The name Heron's formula has been named after the great hero of Alexandria. Also, we can determine the perimeter, semi-perimeter if the parameters mentioned in the formula are given.
We will learn about the application of Heron's formula in this chapter. The famous Heron's formula is
Where a, b, c are the sides of the triangle, and 's' is the semi perimeter of the triangle.
Suppose, in a triangle (any kind of triangle) ABC, all the sides AB, BC, CA are given as 5 cm., 6 cm., 7 cm. First, we have to calculate 's'. 's' can be calculated by the formula
By this formula, we can determine the triangle area, and if the area of the triangle is given, we can determine the length of the sides of the triangle. Moreover, several proofs validate the formula. Apart from Heron, several mathematicians have given some formulas to determine the triangle area for the sake of convenience, but we'll use only Heron's formula in this chapter to understand this formula to the fullest.