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
(C) 2009 Copyright Math Open Reference. All rights reserved
Math Open Reference now has a Common Core alignment.
See which resources are available on this site for each element of the Common Core standards.
Check it out