Area of a triangle (Side-angle-side method)

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)

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

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

How it works

Methods for finding triangle area

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises