• know how to use basic formulas for area and perimeter of a parallelogram. The area is bh where b is the length of the base of the parallelogram and h is the height (perpendicular distance between parallel bases) to that base. The perimeter is found by adding the lengths of the four sides.
• solve basic linear and quadratic equations.
• use the Pythagorean Theorem in finding the length, width, and hypotenuse of a right triangle.
• know basic trig functions and how to use them in a right triangle.

1. 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 > s₂. 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.

 

2. 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.

 

Notice that the side s is the hypotenuse of a right triangle with an angle of 41° opposite the height which is 4. We can use this relationship to find the length of side s as follows:

 

 

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 perimeter is 28.194

 

The area is easy to find since we have the base and height.

 

Area = bh = (8)(4) = 32

 

Once again, a diagram is helpful because it clearly showed the right triangle which allowed us to find the length of the side s.