

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
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
Try this
 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
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
(C) 2011 Copyright Math Open Reference. All rights reserved

