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Transformers

Take any quadrilateral and make it into a triangle without changing the area.

HINT: Parallel lines may be useful.

Place the mouse over the picture below for an illustration.

How many distinct solutions can you find? How many "transformations" were necessary in order to change your quadrilateral into a triangle? Will this always be the case?

 Extensions

Start with any pentagon. Can you convert it into a triangle with equal area?

How many distinct solutions can you find? How many "transformations" were necessary to change your pentagon into a triangle? Will this always be the case?

Try the problem again, but this time with any hexagon.

 Related External Resources

Heron's Area of a Triangle
This site will take you through some historical explorations, some interactive activities, and some intriguing connections in mathematics.

Geoboards in the Classroom
This unit deals with the side lengths and area of two-dimensional geometric figures using the geoboard as a pedagogical device.

Java Explorations (many) [ java applet ]
Explore the Pythagorean Theorem and the minimum distance problem.

Submit your idea for an investigation to InterMath.