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Mathematical known condition
It is known that the quadrilateral ABCD is rectangular, the area of the triangle DEG is 2 cm 2, and the area of the triangle DCG is 3 cm 2.

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.