SOLUTION: In a diagram of a large quadrilateral, AD is parallel to BC, BD is perpendicular to DC, and AE is perpendicular to BD. AB is 41 cm, AD is 50 cm and BF is 9 cm. What is the area o

Algebra ->  Pythagorean-theorem -> SOLUTION: In a diagram of a large quadrilateral, AD is parallel to BC, BD is perpendicular to DC, and AE is perpendicular to BD. AB is 41 cm, AD is 50 cm and BF is 9 cm. What is the area o      Log On


   

Question 25756: In a diagram of a large quadrilateral, AD is parallel to BC, BD is perpendicular to DC, and AE is perpendicular to BD.
AB is 41 cm, AD is 50 cm and BF is 9 cm.
What is the area of the small quadrilateral, DCEF?
Found 2 solutions by venugopalramana, keigan:
Answer by venugopalramana(3286) About Me  (Show Source):
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Answer by keigan(2) About Me  (Show Source):
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The area of DCEF is 960 cm^.
Using Pythagoras, AF = 40cm and FD = 30cm.
Triangles ADF and BFE are similar, so FE = 12 cm.
BD = BF + FD = 39cm.
Triangles BDC and BFE are similar, so DC = 52cm.
DCEF is a trapezium with height DF.
Area of DCEF is ( (FE + DC) x FD) )/2 = 960 cm^.