Area of a triangle - "side angle side" (SAS) method
Drag the orange dots on each
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
a and b are the lengths of two sides of the triangle
C is the included angle (the angle between the two known sides)
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
Substituting this into the top equation we get
Methods for finding triangle area
- In the figure above, click on "hide details"
- Drag the vertices of the triangle to make a new shape
- Calculate the area using this method
- Click "show details" to verify your answer
Related triangle topics
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
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