Heron’s Formula Calculator
Enter the three sides of a triangle to calculate the area using Heron’s formula.
Solution:
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How to use Heron’s Formula
Using Heron’s formula is an easy way to calculate the area of a triangle given the length of the sides. The interior angles of the triangle are not needed to find area using the formula.
For a triangle with three sides a, b, and c, Heron’s formula can be used to find the area.
T = s(s – a)(s – b)(s – c)
Thus, the area T of a triangle is equal to the square root of the semiperimeter s times s minus side a times s minus side b times s minus side c .
The semiperimeter s in Heron’s formula is half the perimeter, so the equation to find s is:
s = a + b + c / 2
After solving the semiperimeter, substitute s in Heron’s formula above.
Alternate Heron’s Formula Equations
Heron’s formula can be simplified or rewritten in a few different ways to solve for area. The following formulas are all derived from Heron’s formula using sides a, b, and c.
T = 1 / 4(a + b + c)(-a + b + c)(a – b + c)(a + b – c)
T = 1 / 42(a²b² + a²c² + b²c²) – (a⁴ + b⁴ + c⁴)
T = 1 / 4(a² + b² + c²)² – 2(a⁴ + b⁴ + c⁴)
T = 1 / 44(a²b² + a²c² + b²c²) – (a² + b² + c²)²
T = 1 / 44a²b² – (a² + b² – c²)²
Our triangle area calculator can also be used to solve for area.
