Constructing a Rectangle with the Same Area as a Pentagon
This Demonstration shows how to construct a rectangle with the same area as that of an arbitrary pentagon . You can drag the vertices of the pentagon.[more]
Draw the diagonal and a parallel to meet at . The triangles and have the same base and the same altitude, so their areas are equal.
Remove from and replace it with to get the quadrilateral , which has the same area as .
Similarly, replace by so that has the same area as , which has an area equal to the area of .
Finally, replace by a rectangle with the same area.[less]
This problem is taken from [1, p. 312], which is a translation from a textbook coauthored by Tarski. The explanation is taken from .
 A. McFarland, J. McFarland and J. T. Smith, eds., Alfred Tarski: Early Work in Poland—Geometry and Teaching, New York: Birkhäuser, 2014.