Inradius Area Formula ðĨ #shorts #science #sigma
The formula Area=r2(a+b+c)Area=2râ(a+b+c) is a geometric expression used to calculate the area of a triangle based on its inradius. The inradius, denoted as rr, is the radius of the incircleâthe largest circle that can fit perfectly inside a triangle, touching all three sides. In this formula, aa, bb, and cc represent the lengths of the triangleâs three sides. When you add these sides and divide by 2, you get the semi-perimeter of the triangle, usually represented by ss. So, the formula simplifies to Area=râ sArea=râ s, meaning the area equals the inradius multiplied by the semi-perimeter. This relationship provides a beautiful link between linear and circular geometry within a triangle. Itâs especially useful in problems where side lengths and inradius are known or easier to find than height or angle information. The formula not only serves practical applications in geometry and trigonometry but also highlights the elegant symmetry within triangle structures.