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Area of Circle Within a Triangle

vCalc Reviewed
`A = pi * (sqrt(( "a" + "b" + "c" )/2(( "a" + "b" + "c" )/2- "a" )(( "a" + "b" + "c" )/2- "b" )(( "a" + "b" + "c" )/2- "c" )) / (( "a" + "b" + "c" )/2))^2`
`(a)"Length Side a"`
`(b)"Length Side b"`
`(c)"Length Side c"`

The Area of Circle Within a Triangle calculator computes the area (blue circle in diagram) of circle that is perfectly inscribed within a triangle.

INSTRUCTIONS: Choose units and enter the following:

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

Area of Circle Within a Triangle (A): The area is returned in square meters and the radius (r) is returned in meters.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for  Area of Circle Within a Triangle equation is:

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

where:

  • A = Area of Circle inscribe within a triangle.
  • a = length of side a
  • b = length of side b
  • c = length of side c

Note: (a+b+c)/2 is the semi-perimeter of the 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