Constructing a Rectangle with the Same Area as a Pentagon
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.
FGHI
ABCDE
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.
CE
DF
AE
F
CED
CEF
CE
Remove from and replace it with to get the quadrilateral , which has the same area as .
CDE
ABCDE
CEF
ABCF
ABCDE
Similarly, replace by so that has the same area as , which has an area equal to the area of .
ACB
ACG
ABCF
GCF
ABCDE
Finally, replace by a rectangle with the same area.
GCF