In order to solve problems which require application of the area
for parallelograms, it is necessary to
A typical problem involving the area
of a parallelogram
gives us the area, perimeter
and/or base, height, and an angle
of the parallelogram. We may also be given a relationship between the area
or between the base
of the parallelogram. We need to calculate some of these quantities given information about the others. Two examples of this type of problem follow:
- Suppose in a parallelogram the base is 8 and the height is 4. What are the area and perimeter of this parallelogram? A diagram is shown below.
Notice that s1
. These parallelograms show two of the infinitely many possible parallelograms with a base
of 8 and a height
We can find the area
of these parallelograms by using A = bh = (8)(4) = 32. We can NOT find the perimeter
because there are infinitely many possible parallelograms that can drawn having different lengths for the other two sides.
Notice the importance of making a diagram (or more than one) to see what is happening when using the given information.
- Suppose a parallelogram has a base of 8, a height of 4, and the side other than the base makes a 41° angle with the base. What are the area and perimeter? A diagram is shown below.
This allows us to find the perimeter
which is the sum of the four sides, two bases of length
8 and two sides of length
is easy to find since we have the base
Once again, a diagram is helpful because it clearly showed the right triangle
which allowed us to find the length
of the side s