Area of a Triangle

One formula for finding the area of a triangle, as stated in an earlier unit, is one-half of the base times the height or Area = . In order to use this formula, we need to know the height of the triangle. There is another formula that can be used if we know two sides and the angle between them. In the triangle below, suppose we know sides a and b and angle C

When a perpendicular line is drawn from the vertex A to side BC, we have the height, h. Because the resulting triangle is a right triangle, we can use the sine function and state:

Solving for h, the result is

h = b sin C

Substituting the new value for h into the original area formula, we obtain:

 Area = ab sin C 2
This formula can be used for finding the area of any triangle.

*Note:  Activity #1 in the overview of this unit is an activity that allows you to derive this formula through investigation.

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