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?

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**