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
- Area of Triangle (base and height)
- Area of Triangle (two sides and interior angle)
- Area of Triangle (two angles and interior side)
- Area of Triangle (three sides)
- Area of Equilateral Triangle
- Area of Triangle (three points)
- Height of Triangle
- Width of Triangle
- Triangle Perimeter
- Interior Angle of a triangle based on the length of three sides
- Semi-perimeter of a triangle
- Area of Circle Within a Triangle
- Area of Circle Around a Triangle
- Area between two vectors
- Triangle Volume
