Transforming a Polygon to a Triangle with Equal Area
Given an arbitrary convex polygon ABCDEF, we construct a triangle with an area equal to the area of the polygon. In a previous article Triangle to Square we showed how any triangle can be transformed to a square with an equal area. The combination of these two constructions shows how to square any convex polygon.
||Repeat the following two steps
until the triangle is constructed:
Press the "Reset" button in the upper right corner, of click again on point F to change the polygon and repeat the constructions.
|1. Click on the
red point F.
This will trigger the following constructions:
2. Click on the point F again.
We see a similar construction. Drag the point F along the doted line as far as it can go. This creates a quadrilateral with an area equal to the area of the pentagon, equal to the original hexagon. The vertex D is eliminated and the polygon becomes a quadrilateral.
3. Click on the point F again.
Following the same steps we transform the quadrilateral to a triangle with the same area.
Press the "Reset" button in the upper right corner to repeat the constructions.
References:H. Eves, An Introduction to the History of Mathematics, Brooks Cole; 6 edition (January 2, 1990)
Irina Boyadzhiev, Created with GeoGebra
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