NCERT Class 9 Maths Lab Manual – Heron’s Formula for Area of a Triangle
To develop the Heron’s formula for area of a triangle.
Concept of triangle and its perimeter.
- A plane figure bounded by three lines sequence is called triangle. The sum of all three sides of a triangle is called perimeter of a triangle.
- In a right triangle, the square of hypotenuse is equal to the sum of the squares of remaining two sides of a triangle.
- Heron’s a mathematician born in Alexandria in Egypt, derived the formula for the area of a triangle in terms of its three sides. This formula is very helpful, where we are not able to find the
height of the triangle. This is generally used for calculating area of scalene triangle.
Let a, b and c be the three sides of a ΔABC and h be the altitude side of a triangle.
Let s be the semi-perimeter of a triangle, then
2s = a+b+c …(i)
Let AD = d, then DB=c – d
In right ΔADC and right ΔCDB,
a² = h²+(c-d)² [by using Pythagoras theorem] …(ii)
a² =h² +c² +d² – 2cd [(A-B)² = A² + B² -2AB] …(iii)
On subtracting Eq. (ii) from Eq. (iii), we get a² -b² =c² -2cd
Given sides of a triangle are 12 cm, 10 cm and 5 cm.
Semi-perimeter of a triangle, s = = ….
Area of triangle by Heron’s formula = = ….
From the above calculation, we conclude that the area of triangle is ………… sq unit.