In order to solve problems which require application of the

area and

perimeter for parallelograms, it is necessary to

A typical problem involving the

area and

perimeter 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 and

perimeter or between the

base and

height 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 s

_{1} > s

_{2}. These parallelograms show two of the infinitely many possible parallelograms with a

base of 8 and a

height of 4.

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 6.097.

The

area is easy to find since we have the

base and height.

Once again, a diagram is helpful because it clearly showed the

right triangle which allowed us to find the

length of the

side *s*.