Triangle Area by Heron’s Formula
Triangle Area by Heron’s Formula
Heron’s formula finds a triangle’s area from its three sides alone — ideal for surveyed plots where no height is measured.
With s = (a+b+c)/2, the area is A = √(s(s−a)(s−b)(s−c)). where a, b, c are the side lengths and s the semi-perimeter.
Inputs
a := 30 m=30 m
b := 40 m=40 m
c := 50 m=50 m
Compute the semi-perimeter.
s := (a + b + c)/2=60 m
Apply Heron’s formula.
A := sqrt(s·(s - a)·(s - b)·(s - c))=600 m^2
Results
This 3-4-5 triangle gives 600 m². Heron’s formula works for any triangle and underlies surveying area calculations.
Assumptions & limitations
- Valid triangle (sides satisfy the triangle inequality).
- Planar triangle.
- Consistent units.