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Area of Triangle (three sides)

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Last modified by
on
Feb 6, 2024, 10:57:30 PM
Created by
on
Jan 4, 2014, 6:36:47 PM
`A = sqrt((a+b+c)/2((a+b+c)/2-a)((a+b+c)/2-b)((a+b+c)/2-c)) `
`(a) "Length of Side a"`
`(b) "Length of Side b"`
`(c) "Length of Side c"`
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The Area of a Triangle from Length of Three Sides calculator computes the area of a triangle given the length of the triangle's three sides using Heron's formula.

INSTRUCTIONS: Choose units and enter the following:

  • (a)  Length of Side a
  • (b)  Length of Side b
  • (c)  Length of Side c 

Area (A): The calculator returns the area in square meters (m2).  However, this can be automatically converted to other area units (e.g. square feet) via the pull-down menu.

The Math / Science

The Heron's formula for the area of a triangle based on the length of the three sides is:

        `A = sqrt((a+b+c)/2((a+b+c)/2-a)((a+b+c)/2-b)((a+b+c)/2-c)) `

where:

  • A is the area of the triangle
  • a is the length of one side
  • b is the length of one side
  • c is the length of one side

The calculator makes a check that no one side is greater than the sum of the other two.  In that case, it is impossible to have a triangle.


A triangle is a polygon with three sides, three vertices (corners), and three angles. Triangles can be classified based on the lengths of their sides and the measures of their angles as follows:

By Side Lengths:

  • Equilateral Triangle: All three sides are equal in length.
  • Isosceles Triangle: Two sides are equal in length.
  • Scalene Triangle: All three sides have different lengths.

By Angle Measures:

  • Acute Triangle: All three angles are less than 90 degrees.
  • Right Triangle: One angle is exactly 90 degrees.
  • Obtuse Triangle: One angle is greater than 90 degrees.

The sum of the interior angles of any triangle always adds up to 180 degrees. 

Triangle Calculators


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