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.*

**Figure 1 **Area of a triangle is half the area of the associated parallelogram.

Finding the Area

Because *A* _{parallelogram} = *bh*, then

Finding the Perimeter

In Δ *ABD* (Figure 1), the perimeter is found simply by adding the lengths of the three sides.

**Example 1:** Find the perimeter and area for the triangles in Figures (a), (b), and (c).

**Figure 2 **Finding perimeters and areas of triangles.

**Example 2:** If the area of a triangle is 64 cm^{2} and it has a height of 16 cm, find the length of its base.

Multiply both sides by 2.

The triangle will have a base of 8 centimeters.