Point E lies on segment AB, and point C lies on segment FG. The area of parallelogram ABCD is 20 square units. What’s the area of parallelogram EFGD?

Source: Alfred S. Posamentier, Math Wonders to Inspire Teachers and Students, 2003.

Let H be the intersection of lines AB and FG.

Using two shear transformations we have

  Area(EFGD) = Area(EHCD) = Area(ABCD) = 20.

QED

Posted by Bractals on 2016-09-19 13:25:12