Find the area of quadrilateral ABGE,
Solution:
Triangle DEG and triangle DCG have the same height on the edge of CE, so their area ratio is the ratio of base length EG and GC:
For example: GC=2:3
As we all know, the rectangles ABCD, AD and BC are parallel, so the triangle EGD is similar to the triangle CGB.
Therefore, ED:BC=EG:GC=2:3.
If the intersection G makes GF perpendicular to CD at point F, then DF:CF=EG:CG=2:3.
Therefore, s △ EGD: s △ CGB = (ed * df/2): (BC * fc/2) = 4: 9.
Therefore, S△CGB=(9/4)*S△EGD=4.5.
Therefore, s delta Abd = s delta BCD = s delta CGB+s delta CGD = 7.5.
Therefore, the area of quadrilateral ABGE = s △ Abd-s △ deg = 5.5cm 2.