Triangle area, three ways
How you find a triangles area depends on what you can measure. This calculator covers the three common cases: base and height, three sides by Herons formula, and two sides with the angle between them. Pick the method that matches your numbers and it returns the area.
The three formulas
Base and height: area = one half times base times height. Three sides (Heron): with s as half the perimeter, area = the square root of s(s-a)(s-b)(s-c). Two sides and the included angle: area = one half times side1 times side2 times the sine of the angle.
Choosing a method
Use base and height when you have a clean perpendicular height. Use Heron when you only know the side lengths. Use the side-angle-side method when you have two sides and the angle wedged between them — common in surveying and layout.
Related geometry tools
For right triangles specifically, the Pythagorean theorem calculator finds missing sides; for many-sided shapes, the regular polygon calculator.
Worked example
A base of 6 and height of 4 give an area of one half times 6 times 4 = 12. The same triangle by Heron, with sides forming that shape, returns the identical area.
FAQ
What if my three sides cannot form a triangle?
If the longest side is at least the sum of the other two, no triangle exists and Herons formula has no real value. The calculator flags this.
Does the angle need to be the included one?
Yes — the side-angle-side area uses the angle between the two sides you enter. A different angle gives a different, incorrect area.