Area of a Triangle Calculator Using Sides – Heron’s Formula

Enter the lengths of the three sides of the Triangle:




How to Calculate Area of a Triangle Using Sides – Heron’s Formula Explained

The area of a triangle is one of the most essential concepts in geometry, useful in fields ranging from architecture and design to land surveying and construction. While the most basic formula—½ × base × height—works only when the height is known, Heron’s Formula allows you to calculate the area of a triangle using just its three sides.

In this guide, we’ll explain how to use Heron’s Formula, illustrate it with an SVG diagram, walk through a few examples, and offer a simple online tool: the Area of a Triangle Calculator to make your calculations even easier.

Formula to Calculate Area of Triangle Using Sides (Heron’s Formula)

Given the sides of a triangle are:

  • a, b, and c

Step 1: Calculate the semi-perimeter (s):

s = (a + b + c) / 2

Step 2: Apply Heron's Formula:

Area = √[s(s - a)(s - b)(s - c)]

This method works for any triangle (scalene, isosceles, or equilateral), as long as the side lengths form a valid triangle.

Example 1: Triangle with Sides 7, 8, and 9 Units

a = 7, b = 8, c = 9

Step 1: Semi-perimeter

s = (7 + 8 + 9) / 2 = 12

Step 2: Apply formula

Area = √[12 × (12 - 7) × (12 - 8) × (12 - 9)]
     = √[12 × 5 × 4 × 3] = √720 ≈ 26.83 square units

Example 2: Equilateral Triangle with Sides 10 Units

a = b = c = 10

Step 1: Semi-perimeter

s = (10 + 10 + 10) / 2 = 15

Step 2: Apply formula

Area = √[15 × 5 × 5 × 5] = √1875 ≈ 43.30 square units

SVG Diagram of a Triangle

c b a A B C

Use the Online Calculator

Manually calculating the area of a triangle with sides can be time-consuming and prone to error. That’s why we’ve built a free and easy-to-use tool for you.

Try the Area of Triangle Calculator

Tips & Considerations

  • Ensure the side lengths follow the triangle inequality rule: a + b > c, a + c > b, b + c > a.
  • If side lengths are in centimeters, the area will be in square centimeters.
  • This method works for all triangle types: scalene, isosceles, and equilateral.

Real-World Applications

  • Land Surveying: Use Heron’s formula when triangle heights are not available.
  • Architecture: Useful in triangular supports or roof design.
  • Mathematics: Common in competitive exams and geometry problems.

Recap

To calculate the area of a triangle using side lengths:

  1. Find the semi-perimeter s = (a + b + c)/2
  2. Use the formula Area = √[s(s - a)(s - b)(s - c)]
  3. Use our calculator for quick results!

Try it now with our Area of Triangle Calculator