Triangle area formula
Triangle area: triangle with base and height
A triangle is one of the most basic shapes in geometry. The best known and the most straightforward formula, which almost everybody remembers from school, is:
area = 0.5 * b * h, where b is the length of the base of the triangle, and h is the height/altitude of the triangle.
However, sometimes it's hard to find the height of the triangle. In that cases, many other equations may be used, depending on what you know about the triangle:
Triangle area: triangle with three sides
Three sides (SSS)
If you know the lengths of all sides, use the Heron's formula:
area = 0.25 * √( (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) )
Triangle area: triangle with two sides and angle between them (SAS)
Two sides and the angle between them (SAS)
You can calculate the area of a triangle easily from trigonometry:
area = 0.5 * a * b * sin(γ)
Triangle area: triangle with two angles and side between them (ASA)
Two angles and a side between them (ASA)
There are different triangle area formulas versions - you can use, for example, trigonometry or law of sines to derive it:
area = a² * sin(β) * sin(γ) / (2 * sin(β + γ))
If you are looking for other formulas or calculators connected with triangles, check out this right triangle calculator, pythagorean theorem calculator, and law of cosines calculator.