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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?
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Area of a parallelogram = h x b
h= 4 ft b=6 ft
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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.
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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.
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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?
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Area of a parallelogram = h x b
h= 3 ft b= 7 ft
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3 ft x 7 ft = 21ft^2
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