Area of a parallelogram - derivation
This page describes how to derive the formula for the
area of a parallelogram. It works by moving a piece of the parallelogram
so as to make a rectangle with the same area, which is easier to calculate.
- Start with a parallelogram with known
length (width) w and
altitude h (height).
- Cut off a triangular section.
- Translate (move) the copy to touch the original so as to create a rectangle.
Click on the "Run" button below to see this in action.
This rearranging has created a rectangle whose area is clearly the same as the original parallelogram.
Recall that the
area of a rectangle is found by multiplying its width times its height. The area of the original parallelogram is therefore
w is the width, or length of a base, and
h is the altitude (height) of the parallelogram.
Related polygon topics
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
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