perimeter of triangle

Obtaining the Area of a Triangle Using Heron’s Formula


Heron’s formula also called as Hero’ s formula (named after “Hero of Alexandria”) a well-known mathematician, defined a formula that can be used to find the area of a triangle when all the sides of a triangle are given. It is applied to all types of the triangle such as scalene triangles, isosceles triangle and equilateral triangle. To find the area of a triangle, the first thing is to calculate half the value of perimeter or semiperimeter of a triangle and it is represented as ‘s’. Consider ABC be a triangle and a, b, and c represents the sides of a triangle and the perimeter of triangle is defined as the sum of the sides of a triangle, a + b + c

Then, the semi-perimeter of a triangle is given by

                    s = Perimeter of a triangle/2 = ( a + b + c ) / 2

Hence, the Heron’s formula is defined as

                    A2 = s ( s – a)x(s – b)x(s – c)

Where,    A = Area of a triangle

       s = semi-perimeter of a triangle

 a, b and c = Sides of a triangle

It is noted that always height is needed to find out the area of a triangle. But it is exceptional in Heron’s formula. Only the sides of a triangle is enough to calculate the area of a triangle. The proof of Heron’s formula is derived using cosine law in trigonometry or by using algebraic proof. In trigonometric proof, use factorisation instead of using multiplication, because multiplication consumes lot of time when the identities are applied to the law of cosines. The equivalence of Heron’s formula is also given by the Pythagorean theorem after getting the factors of s(s-a) x (s-b)(s-c). Heron’s formula is also applied to find the area of quadrilaterals. In such cases, the quadrilaterals are divided into triangles to find the area. The result will be the same when you compare the area of a triangle using Heron’s formula and area of the triangle using the formula A = bh/2

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