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Circumference, Area,
Surface Area, and Volume
By Taylor Winter
Derive the Formula:
Area of a Parallelogram
Example Problems
1. A parallelogram has a base length of 6 ft and a height of 4 ft. What is the area of this parallelogram?
Area of a parallelogram = h x b
h= 4 ft b=6 ft
4 ft x 6 ft = 24 ft^2
To find the formula we need 2 principles:
-The moving principle states that if you move a shape rigidly without stretching or shrinking the area remains the same.
-The additive principle states that if you combine shapes without overlapping them then the area of the resulting shape is the sum of the areas of the individual shape.
So looking at the figure to the side you can see how a parallelogram through moving and additive principle can be made into a rectangle. Therefore the area of a parallelogram is the same as area of a rectangle,
or height x base.
2. Ms. Smith created a garden in the shape of a parallelogram. The plants are all one foot away from each other and there are 7 plants in each row and 3 rows. What is the area of her garden?
Area of a parallelogram = h x b
h= 3 ft b= 7 ft
3 ft x 7 ft = 21ft^2
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