What is the area of the shaded region? A 13,928.142 sq mm
B 20,378.126 sq mm
C 15,873.023 sq mm
D 16,682.522 sq mm

its d d d d d d d. d d d d d d. d d d d d. d d d d d d d d d d d d d d. d d d

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4