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 Subdivided parallelogram (Posted on 2019-03-04)
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 No Rating

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 step 2 - an answer | Comment 3 of 6 |
Here is the second part. I see armando posted in the meantime. Will we agree? I don't know...

I used the 10 x 12 rectangle and have sides for the quad. broken into two triangles:

1)BT=sqrt(9^2+4^2), BS=sqrt(4^2+8^2), TS=1
2)TD=sqrt(3^2+6^2), SD=sqrt(6^2+4^2), TS=1

and using Heron's Formula of form
Area= 1/4 sqrt(4 a^2 b^2-(a^2+b^2-c^2) )

Area = area 1 + area 2 = 2 + 3 = 5
I get Area = 5. I see armando did too. And, I think he caught on a lot sooner than I did!

Edited on March 5, 2019, 9:42 pm
 Posted by Steven Lord on 2019-03-05 18:03:27

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