Heron's formula


You can use Heron's formula to calculate the area of any triangle when you know the lengths of the three sides.

If you call the lengths of the three sides a, b, and c, the formula is :

A-triangle-image




A-triangle-image




S is called the semi-perimeter. The name makes sense because it is the perimeter divided by two.

Example #1:

Use Heron's formula to find the area of a triangle when a = 3 cm, b = 5 cm, and c = 4 cm

s = (3 + 5 + 4)/2 = 12/2 = 6

s − a = 6 − 3 = 3

s − b = 6 − 5 = 1

s − c = 6 − 4 = 2

s × (s − a) × (s − b) × (s − c) = 6 × 3 × 1 × 2 = 36

√(36) = 6

The area of this triangle is 6 cm2


Example #2:


Find the area of a triangle when a = 4 cm, b = 6 cm, and c = 8 cm

s = (4 + 6 + 8)/2 = 18/2 = 9

s − a = 9 − 4 = 5

s − b = 9 − 6 = 3

s − c = 9 − 8 = 1

s × (s − a) × (s − b) × (s − c) = 9 × 5 × 3 × 1 = 135

√(135) = 11.61

The area of this triangle is 11.61 cm2


Example #3:


Find the area of a triangle when a = 3/2 cm, b = 5/2 cm, and c = 2 cm

s = (3/2 + 5/2 + 2)/2 = (3/2 + 5/2 + 4/2)/2 = (12/2)/2 = 6/2 = 3

s − a = 3 − 3/2 = (6/2 − 3/2) = (6 − 3)/2 = 3/2

s − b = 3 − 5/2 = (6/2 − 5/2) = (6 − 5)/2 = 1/2

s − c = 3 − 2 = 1

s × (s − a) × (s − b) × (s − c) = 3 × 3/2 × 1/2 × 1 = 9/4

√(9/4) = 3/2

The area of this triangle is 1.5 cm2







Recent Articles

  1. Fractions - Basic Mathematics

    Apr 02, 19 05:34 PM

    Learn about equivalent, benchmark, multiplying, dividing, adding and subtracting fractions

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Math quizzes

 Recommended

Scientific Notation Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz

Types of angles quiz


Tough algebra word problems

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Recent Articles

  1. Fractions - Basic Mathematics

    Apr 02, 19 05:34 PM

    Learn about equivalent, benchmark, multiplying, dividing, adding and subtracting fractions

    Read More

K-12 math tests


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.