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.