# Heron's Formula Class 9

Area of a triangle is given by $\frac{1}{2}\times base\times altitude$.. If a given triangle is a right angle triangle then, we can apply the above formula for evaluating the area of triangle by using two sides containing the 90 degree angle as height and base. For finding the area of an equilateral triangle of side ‘a’ we need to find its height by breaking the equilateral triangle into two right triangles. Now, by using Pythagoras Theorem, we can easily evaluate the length (l) followed by its area. Same procedure can be followed for finding the area of an isosceles triangle. However, it’s difficult to find the area of a scalene triangle without knowing its height.

Area of a Triangle — by Heron’s Formula

The area of a scalene triangle can be easily evaluated by the formula given by Heron known as Heron’s formula. If a, b, c are length of sides of a triangle, then, from Heron’s formula:

Area of a triangle = s(s − b) (s − a) (s − c), Where s is semi-perimeter i.e. half the perimeter of the triangle. By dividing the quadrilateral into two halves we can easily evaluate the area of a quadrilateral by applying Heron’s Formula using the length of its sides and one of its diagonal.

### Heron’s Formula class 9 Examples

#### Practise This Question

In a marathon of 5 km, Manish could run for 2 km.If  Kushagra ran for 12 of the total length of the marathon, who covered more distance?