Squaring a Convex Polygon

This applet constructs a triangle with an area equal to the area of any convex polygon ABCDEF. The applet Squaring a Triangle shows 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.

• Click on point F.
• Drag F to the right as far as it can go.
• Repeat these two steps three times, until the triangle is constructed.

To repeat the construction,  press the "Reset" button or click again on the vertex F of the triangle.

Author: Irina Boyadzhiev   The Ohio State University at Lima
For more details click here.

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Squaring a Triangle

This applet shows the construction of a square with the same area as a given triangle.
This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Author: Irina Boyadzhiev of Ohio State University.

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Area of a Trapezoid

Move point A to change the shape of the trapezoid.  Then move slider  to the extreme right to rotate the trapezoid.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1.) What kind of quadrilateral  is formed when  equals 180 degrees? Justify your answer.
2.) What is the relationship between the area of trapezoid ABCD and the area of the quadrilateral formed in 1?
3.) Using the quadrilateral formed in 1, find the area of the trapezoid. Hint: Use  and .


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