Theory

Finding the area of a triangle

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram below, the area of each triangle is equal to one-half the area of the parallelogram.

 

 

 


 

Since the area of a parallelogram is A = b x h, the area of a triangle must be one-half the area of a parallelogram. Thus, the formula for the area of a triangle is:
or

where b is the base, h is the height and · means multiply.

 

 

 
 
The base and height of a triangle must be perpendicular to each other. In each of the examples below, the base is a side of the triangle. However, depending on the triangle, the height may or may not be a side of the triangle. For example, in the right triangle in Example 2, the height is a side of the triangle since it is perpendicular to the base. In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.