Area of a triangle - "side angle side" (SAS) method

where a,b are the two known sides and C is the included angle.
Try this Drag the orange dots on each vertex to reshape the triangle. The formula shown will recalculate the area using this method.

Usually called the "side angle side" method, the area of a triangle is given by the formula below. Although it uses the trigonometry Sine function, it works on any triangle, not just right triangles. where
a and b  are the lengths of two sides of the triangle
C  is the included angle (the angle between the two known sides)


Side 1 clear
Side 2 clear
Angle (degs) clear

Use the calculator above to calculate the area of a triangle given 2 sides and the angle between them.

How it works

This method is really just an extension of the regular "half base times height" method.
In the figure above, the area would be given by the formula But we are not given h - the height. But we are given the side a and the angle C. We know that Transposing Substituting this into the top equation we get

Methods for finding triangle area

If you know: Use this
Base and altitude "Half base times height" method
All 3 sides Heron's Formula
Two sides and included angle Side-angle-side method
x,y coordinates of the vertices Area of a triangle- by formula (Coordinate Geometry)
Area of a triangle - box method (Coordinate Geometry)
The triangle is equilateral Area of an equilateral triangle

Try this

  1. In the figure above, click on "hide details"
  2. Drag the vertices of the triangle to make a new shape
  3. Calculate the area using this method
  4. Click "show details" to verify your answer

Other triangle topics


Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises