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)

## Calculator

 ENTER TWO SIDES AND INCLUDED ANGLE Side 1 clear Side 2 clear Angle (degs) clear Area:

Use the calculator on the right to calculate the area of a triangle given 3 sides using Heron's formula.

Enter the three side lengths and press 'Calculate'. The area will be calculated.

## 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

## Related triangle topics

### Triangle quizzes and exercises

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