In the parallelogram shown in Figure
1 ,
h is a height because it is perpendicular to a pair of opposite sides called
bases. One of the bases has been labeled
b, and the nonbase remaining sides are each labeled
a.
|
|
|
|
|
Figure 1
|
A parallelogram with base and height labeled.
|
|
|
Finding the perimeter
The following formula is now apparent.
Finding the Area
In Figure
1 , also notice that Δ
WXV ≅ Δ
TYZ, which means that they also have equal areas. This makes the area of
WXYT the same as the area of
XYZV. But
Arectangle
XYZV =
bh, so
Aparallelogram
XYTW =
bh. That is, the area of a parallelogram is the product of any base with its respective height.
Example 1: Find the perimeter and area of Figure
2 .
|
|
|
|
|
Figure 2
|
Finding the perimeter and area of a parallelogram.
|
|
|
The figure is a parallelogram, so
Fundamental Ideas
Perimeter and Area
