Area of Quadrilateral inside a rectangle

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To find the area of quadrilateral CDGE within a rectangle, the area can be divided into triangles by drawing line DE. The area ratios of triangles ABE to ECD is established as 4:1, while the ratios of triangles ADG to DGE and ADG to AGF depend on the lengths AG, GE, DG, and GF. A suggestion is made to extend lines AE and DC to find their intersection point H, which may aid in further calculations. The discussion highlights the importance of visualizing geometric relationships to solve area problems effectively. Understanding these relationships is crucial for determining the area of the quadrilateral accurately.
songoku
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Homework Statement
Please see the picture below.

If AF = FB, BE = 4CE and the area of AGD = 100, find the area of CDGE
Relevant Equations
Not sure
1673404002767.png


I try to divide the area of CDGE into two areas of triangles by drawing line DE.

The ratio of area of triangles ABE and ECD = 4 : 1

The ratio of area of triangles ADG and DGE = AG : GE

The ratio of triangles ADG and AGF = DG : GF

Then I don't know what to do.
 
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Why don't you extend AE and DC and observe they cross ,say, at H ?
 
Last edited:
anuttarasammyak said:
Why don't you extend AE and DC and observe they cross ,say, at H ?
I understand your hint. Thank you very much anuttarasammyak
 

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