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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.

  1. Start with a parallelogram with known base length (width) w and altitude h (height).
  2. Cut off a triangular section.
  3. 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 where
w is the width, or length of a base, and
h is the altitude (height) of the parallelogram.

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Other polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons