NCERT Notes for Class 9 Maths Chapter 7 Heron's Formula
Class 9 Maths Chapter 7 Heron's Formula Notes
Chapter Name  Heron's Formula Notes 
Class  CBSE Class 9 
Textbook Name  NCERT Mathematics Class 9 
Related Readings 

Perimeter
It is the outside boundary of any closed shape. To find the perimeter we need to add all the sides of the given shape.
The perimeter of a rectangle is the sum of its all sides. Its unit is same as of its length.
Perimeter = 3 + 7 + 3 + 7 cm
Perimeter of rectangle = 20 cm
Area of different Triangles
Area of any closed figure is the surface enclosed by the perimeter. Its unit is square of the unit of the length.
Area of a triangle
The general formula to find the area of a triangle, if the height is given, is
Here base = 3 cm and height = 4 cm
Area of triangle = 1/2 × 3 × 4
= 6 cm^{2}
Remark: If you take base as 4 cm and height as 3 cm then also the area of the triangle will remain the same.
Area of Equilateral Triangle
If all the three sides are equal then it is said to be an equilateral triangle.
In the equilateral triangle, first, we need to find the height by making the median of the triangle.
Here, the equilateral triangle has three equal sides i.e. 10 cm.
If we take the midpoint of BC then it will divide the triangle into two right angle triangle.
Now we can use the Pythagoras theorem to find the height of the triangle.
AB^{2} = AD^{2} + BD^{2}
⇒ (10)^{2} = AD^{2} + (5)^{2}
⇒ AD^{2} = (10)^{2} – (5)^{2}
⇒ AD^{2} = 100 – 25 = 75
⇒ AD = 5√3
Now, we can find the area of triangle by
Area of triangle = 1/2 × base × height
= 1/2 × 10 × 5√3
25√3 cm^{2}
Area of Isosceles Triangle
In the isosceles triangle also we need to find the height of the triangle then calculate the area of the triangle.
Here,
Area of a Triangle by Heron’s Formula
The formula of area of a triangle is given by heron and it is also called Hero’s Formula.
Here, the sides of triangle are
AB = 12 cm
BC = 14 cm
AC = 6 cm
Application of Heron’s Formula in Finding Areas of Quadrilaterals
If we know the sides and one diagonal of the quadrilateral then we can find its area by using the Heron's formula.
Find the area of the quadrilateral if its sides and the diagonal are given as follows.
Given, the sides of the quadrilateral
AB = 9 cm
BC = 40 cm
DC = 28 cm
AD = 15 cm
Diagonal is AC = 41 cm
Here, ∆ABC is a right angle triangle, so its area will be
Area of Quadrilateral ABCD = Area of ∆ABC + Area of ∆ADC
= 180 cm^{2} + 126 cm^{2}
= 306 cm^{2}