Look at Δ ABD in Figure 1. If a line BC is drawn through B parallel to AD and another line DC is drawn through D parallel to AB , then you will have formed a parallelogram. BD is now a diagonal in this parallelogram. Because a diagonal divides a parallelogram into two congruent triangles, the area of Δ ABD is exactly half the area of
ABCD.
![](http://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18223.jpg)
Figure 1 Area of a triangle is half the area of the associated parallelogram.
Because A parallelogram = bh, then
![](https://s3.amazonaws.com/dev-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18203.jpg)
In Δ ABD (Figure 1), the perimeter is found simply by adding the lengths of the three sides.
![](https://s3.amazonaws.com/dev-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18204.jpg)
Example 1: Find the perimeter and area for the triangles in Figures (a), (b), and (c).
![](http://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18224.jpg)
Figure 2 Finding perimeters and areas of triangles.
![](https://s3.amazonaws.com/dev-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18205.jpg)
Example 2: If the area of a triangle is 64 cm2 and it has a height of 16 cm, find the length of its base.
![](https://s3.amazonaws.com/dev-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18206.jpg)
Multiply both sides by 2.
![](https://s3.amazonaws.com/dev-hmhco-vmg-craftcms-public/_cliffsnotes/assets/18207.jpg)
The triangle will have a base of 8 centimeters.