Geometry

Heron's Formula

Formula

A = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2

What is Heron's Formula?

Heron's formula calculates the area of a triangle when all three sides are known, without needing the height. The semi-perimeter s is half the perimeter.

Variables

A
A — Area of the triangle
s
s — Semi-perimeter = (a+b+c)/2
a
a, b, c — Three sides of the triangle

Worked Examples

Example 1

Find the area of a triangle with sides 5, 12, and 13.

Solution:

s = (5+12+13)/2 = 15. A = √(15×10×3×2) = √900 = 30 cm²

Frequently Asked Questions

Related Formulas

Area of a Circle

A = π × r²

Circumference of a Circle

C = 2 × π × r

Area of a Rectangle

A = l × w

Area of a Triangle

A = ½ × b × h

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