Heron’s formula
Introduction to heron’s formula
Introduction of another formula for
area of a triangle
• Most of us are aware with :
• Area of a triangle =
Where b = base and h = corresponding height
of the triangle
Examples :
• 1) Find the area of a triangle having sides :
AB = 4 cm
BC = 3 cm
CD = 5 cm
Solution of Example 1)
Continue…
Example 2:
2) Rahul has a garden, which is triangular in
shape. The sides of the garden are 13 m, 14 m,
and 15 m respectively. He wants to spread
fertilizer in the garden and the total cost
required for doing it is Rs 10 per m2. He is
wondering how much money will be required to
spread the fertilizer in the garden
Solution of Example 2)
• Given a = 13 m , b = 14 m and c = 15 m
So , we will find
the area of the
triangle by
using Heron’s
formula.
Continue..
21(21  13)(21  14)(21  15)
=
21*8* 7 * 6
Continue …
• Given the rate = Rs 10 per m^2
• Now :
• Total cost = Rs. 10 * 84 = Rs 840/-
Area of a quadrilateral
• Suppose there is a quadrilateral
having sides : a , b , c and d and
diagonal r.
The diagonal d divides the quadrilateral into 2
triangles.
So : Ar(ABCD)= Ar(ABD) + Ar(BCD)
Continued
1) Area of triangle : ABD
Heron’s formula:
Putting the values we get :
Continued..
Solution of example
As we have the formula written below for the
area of a quadrilateral
Where :
a = 4cm
b = 3 cm
c = 5 cm
d = 6 cm
And r (diagonal ) = 7 cm
cm2
Click on this arrow to continue
How to find the area of an equilateral
triangle
Concept based question
• What equilateral triangle would have the
same area as a triangle with sides 6, 8 and 10?
Solution
• First of all we will find the area of the triangle
having sides : a = 6 units , b = 8 units and c =
10 units