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# What is Heron’s Formula?

Maths | 7-14 yrs | Interactive

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

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

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