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Home >> Triangle >> Area of Triangle by Heron's Formula >>

Heron's Formula to find Area of Triangle

Properties Types / Classification Perimeter of Equilateral Triangle Median of Triangle Interior of a Triangle
Exterior of a Triangle Altitude of a Triangle Interior Angles of Triangle Exterior Angles of Triangle Interior Opposite Angles of Triangle
Adjacent Interior Angle of Triangle Congruent Triangles Area of Triangle Area of Triangle by Heron's Formula Construction of Triangle (compass)

Before you understand Heron's Formula, you are advised to read:

How to find Area of Triangle ?
What is Perimeter ?
What is Square-Root ?

As you know that:
Area of Triangle = 1/2 X Base X Altitude

But you may encounter some situation where you do not have the value of altitude. So in such situation, where altitude is unknown, Heron's formula is used to calculate Area of Triangle.

Heron's Formula was given by a famous Egyptian Mathematician Heron in about 10AD and therefore this formula was also named after him.

Heron's Formula = s (s-a) (s-b) (s-c)

In the above formula:
a, b and c are the three sides of a triangle
s is semi-perimeter i.e. half of the perimeter
or we can write it as:
s = a + b + c
2


Example: Find the area of following triangle:



Solution: As per the given question:
Three sides of given Triangle ABC are AB, BC and CA
AB = 28 cm = a
BC = 15 cm = b
CA = 41 cm = c

Semi-perimeter of Triangle ABC =
a + b + c
2


Apply the values of AB, BC & CA and we get:
s = 28 + 15 + 41
2


Solve addition in the numerator and we get:
s = 84
2


Solve division expression and we get:
= 42
So, s = 42

Apply Heron's Formula = s (s-a) (s-b) (s-c)

Apply the values of s, a, b & c and we get:
= 42 (42-28) (42-15) (42-41)

Solve brackets and we get:
= 42 (14) (27) (1)

Solve square-root and we get:
= 126

Hence, Area of Given Triangle ABC = 12cm2


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