Heron’s formula, sometimes known as Hero’s formula is named after Hero of Alexandria, a mathematician, and engineer in 10 AD.
Definition for Heron’s formula
Heron’s formula gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas that calculate the area of a triangle. The area can be calculated using all the three sides, especially in scalene triangle, where none of the sides are equal. Most formulas use the height of a triangle to calculate the area.
What are the steps for Heron’s formula?
According to this formula,
Area of the triangle –
where the semi – perimeter of the triangle,
a, b, c are the lengths of the sides of the triangle.
Heron’s Formula Worksheet
1. Calculate the semiperimeter of a triangle, s, where a = 23, b = 40, c = 35.
a. 35
b. 48
c. 25
d. 49
Right Answer- d. 49
2. Calculate the area of a triangle using Heron’s formula, if the three sides of the triangle are, a = 5, b = 9, c = 6
a. 12.34
b. 10.6
c. 14.14
d. 13.26
Right Answer- 14.14
3. Calculate the side of a triangle b, if side a = 12 and side c = 6 and the semi – perimeter equals 13.
a. 9
b. 8
c. 6
d. 7
Right Answer- b. 8
3 Interesting facts about Heron’s Formula
- Heron’s formula has been known to mathematicians for nearly 2000 years.
- Proof of this formula can be found in Hero of Alexandria’s book “Metrica”.
- Many mathematicians believe that Archimedes already knew the formula before Heron. Some also believe that this formula has Vedic roots and the credit should be given to the ancient Hindus.