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Dividing a Rectangle (Posted on 2009-07-25) Difficulty: 2 of 5

Points E and F lie on the sides AB and AD respectively of rectangle ABCD
(not the corners). The line segments BF, FC, CE, and ED divide ABCD into
six triangles and two quadrilaterals. BF intersects CE and DE at points P 
and Q respectively. CF intersects ED at point R.

Let [WX...Z] denote the area of polygon WX...Z.
If [AEQF] = 35, [BPE] = 9, and [DFR] = 6; then what is [CRQP] ?

  Submitted by Bractals    
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Solution: (Hide)

                    [CDE] = [ABCD]/2 = [ABF] + [CDF]

   [CDR] + [CRQP] + [EPQ] = ( [AEQF] + [BPE] + [EPQ] ) + ( [CDR] + [DFR] )

                   [CRQP] = [AEQF] + [BPE] + [DFR]

                          = 35 + 9 + 6

                          = 50

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle ThoughtsK Sengupta2023-12-27 08:01:14
Puzzle Thoughts K Sengupta2023-06-19 22:19:05
solutionDaniel2009-07-25 15:21:25
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