1. Fill up the 6-by-6 square using these 6 polygons:
   • Rectangle with area 12 and perimeter 14
   • Rectangle with area 12 and perimeter 16
   • Rectangle with area 3 and perimeter 8
   • Right triangle with area 3 and base 2
   • Right triangle with area 1
   • Triangle with area 4
     

   

2. Assemble the following polygons to form the same 6-by-6 square as above.
   • Right angle trapezoid with area 5
   • Trapezoid with area 3
   • Right angle trapezoid with area 13
   • Trapezoid with area 12
   • Rectangle with dimensions 1 by 2
     Put the rectangle somewhere in the middle.
     

Hint to problem 2. Actually, all of the trapezoids will have at least one 90^o angle, and all but one will have two 90^o angles.

Slightly different arrangements are possible for these.