Triangle from three sides
Area (Heron's formula) and angles of a triangle from its sides only: useful to survey land with a string.
Tool
Tools › Geometry and measurement
How it is calculated
Heron's formula: with s = (a + b + c) ÷ 2 (the semi-perimeter), area = √(s × (s − a) × (s − b) × (s − c)).
Worked by hand: sides of 30, 40 and 50 m → s = 60; area = √(60 × 30 × 20 × 10) = √360,000 = 600 m².
The angles come from the law of cosines: cos A = (b² + c² − a²) ÷ (2 × b × c).
Keep in mind
- To survey a plot of any shape: drive stakes at the corners, split it into non-overlapping triangles, measure the sides with a tight string or chain and add the areas.
- Avoid very flat triangles (an angle under about 20°): a small error in one side changes the area a lot.