Area of ​​a Triangle (Heron's Formula)

Heron's formula is a formula that uses only the lengths of the three sides of a triangle to find the area. It is widely used as a convenient formula because it can be calculated without knowing the height or the length directly. The formula was created after the ancient Greek mathematician Heron of Alexandria.

Heron's formula

Let the lengths of the three sides of a triangle be "a", "b", and "c". In this case, the "area: S" is calculated using the following procedure.

Calculate "semi-perimeter: s"

s is half the perimeter of the triangle.

s = (a + b + c)/2

Calculate "area: S"

S = √(s × (s - a) × (s - b) × (s - c))

Calculate Heron's formula

Calculate the area of ​​a triangle with sides a=5, b=6, c=7.

Calculate "semi-perimeter: s"

s is half the perimeter of the triangle.

s = (5 + 6 + 7) / 2 = 9

Calculate "Region: S"

S = √(9 × (9 - 5) × (9 - 6) × (9 - 7)) = √216 ≒ 14.7