Calculate triangle area, perimeter, angles, and other properties using sides, base & height, or two sides with included angle.
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A triangle is a polygon with three sides and three angles. The sum of all angles in a triangle is always 180°. Key formulas include Heron's formula for area from three sides, the basic area formula (½ × base × height), and the law of cosines for finding sides and angles.
Heron's Formula
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Step-by-step solutions for learning
Heron's formula calculates a triangle's area using only the three side lengths: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2. It's useful when you don't know the height.
Three sides form a valid triangle if and only if the sum of any two sides is greater than the third side. This is called the triangle inequality theorem.
The inradius (r) is the radius of the largest circle that fits inside the triangle (inscribed circle). The circumradius (R) is the radius of the circle that passes through all three vertices (circumscribed circle).
It uses Heron's formula. First it computes the semi-perimeter s = (a + b + c) / 2, then the area A = √(s(s−a)(s−b)(s−c)). For a 3-4-5 triangle, s = 6 and A = √(6 × 3 × 2 × 1) = √36 = 6. This calculator also reports the perimeter, all three angles, the inradius, and the circumradius.