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Subdivided parallelogram (Posted on 2019-03-04) Difficulty: 2 of 5
Let ABCD be a parallelogram. Draw QN parallel to AB with Q lying on AD and N lying on BC. Draw another line MS parallel to AD with M lying on AB and S lying on QN. Draw yet another line PT parallel to AD with P lying on CD and T lying on QN.

The area of AMSQ, BNSM, CPTN and DQTP are respectively 12, 36, 48, and 24. What is the area of quadrilateral BSDT?

No Solution Yet Submitted by Danish Ahmed Khan    
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My take | Comment 2 of 6 |
I think it will be the same for a rectangle as the area of each parallelogram is the same as the area of a rectangle with the same height of the parallelogram. The distance between the different points will change but the area between a set of points like a quadrilateral won't change. 

Drawing the rectangle you can know from the area of each parallelogram the lenght of each segments of points. 

From there is very easy. In terms of area

BTS=BNTM -BMS -BNT=2
TDS=QDPT -QDS -TPD=3

BSDT=5



  Posted by armando on 2019-03-05 16:20:50
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