WOLFRAM|DEMONSTRATIONS PROJECT

The Quadrilateral of Centroids

area(EFGH)

≈

20.06

9 area(EFGH)

≈

180.57

area(ABCD)

≈

180.57

Let ABCD be a quadrilateral and E, F, G and H be the centroids of the triangles ABC, BCD, ACD, and ABD. Then 9×area(EFGH) = area(ABCD). Also EF

||

AD, FG

||

AB, GH

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BC and EH

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CD.