The question is:
ABCD is a parallelogram and BFDE is a square . If AB is 20 and CF is 16 what is the perimeter of the parallelogram.
The question is fairly simple and I know how to solve it. However how would I get the remaining angles of triangle FDC (highlighted) if i know that CD=20 and FD=12. I also know that angle F is 90 however the triangle doesn't seem to be 30-60-90 or a 45-45-90. Also I need to solve this without Trigonometric ratios since I wont be using calculator
The triangles $\,ABE\,,\,CDF\,$are congruent, thus $\,CD=20\,$. Apply now Pythagoras and get $\,FD^2=20^2-16^2=144\Longrightarrow FD=12=FB=ED\,$ , so $\,AD=BC=16+12=32\,,\,AB=CD=20\,$ and now just add.