Dragan

Let the side of the square be 4 inits.

DF = tan(20º) * 4  = 1.455880937

FC = 4 - DF = 2.544119063

BE = tan(25º) * 4 = 1.865230633

EC = 4 - BE = 2.134769367

tan(∠FEC) = FC / EC          ∠FEC = 50º

∠X = 180º - (65º + 50º) =  65º    

Let the crosspoint of the diagonals of the rhombus be an N.

Let the crosspoint of AD and BF be an M

BN = [sqrt(2² + 3²)] / 2 = 1.802775638

tan(∠FBD) = 2 / 3             ∠FBD = 33.69006753°

NM = BN * tan(∠FBD)   =   1.201850425

Shaded area       A= ( BN * NM ) * 2  =  4.3333333333 units squared  

It's not that simple!

AB = 11.84846923    

87 / 60 = (2x + 80) / 80

60 ( 2x + 80 ) = 87 * 80

120x + 4800 = 6960

120x = 6960 - 4800

120x = 2160

x = 2160 / 120  

x = 18     

Proof:        (27 + 60) / (2*18 + 80) = 0.75                      60 / 80 = 0.75      

x = 360° - 90° - 90° - 20° = 160°  

This is real math! 

The area of the square is       A = 256 u²  

In rectangle ABCD, AB = 3 and BC = 5.  The corner at C is folded up and lands on AB so that AC = 2 and BC = 1.  Find the area of quadrilateral CPNM.

The area of quadrilateral CPNM  is:                A ≈ 6.067 u²  

Split green square in half; we have 2 identical rectangles. Rectangle's diagonal is the radius of the semi circle.

Ratio of rectangle's short side to long side is  1 : 2

The angle between the radius and the longer rectange side is     tan(A) = 1 / 2 = 26.56505118°

Let the radius  r = 1

Green square side    a = cos(A) = 0.894427191

Green  area          A_g = a² = 0.8 u²

Blue square diagonal is the radius and it is also  r = 1

Blue square side      b = sqrt(1/2) = 0.707106781

Blue  area              A_b = 2 * b² = 1 u²   

The ratio of the  green  area to the  blue  area is  4 : 5  

If  PN = 4 than AN = 12        ( see diagram )

If  AN = 12  than AM = 36

If  AM = 36  than  the side  AB = AM / sin(60°) = 41.56921938

41.56921938 / sqrt(3) = 24

The side length of the equilateral triangle is     24*sqrt(3)