Divide the rectangle in the above way, to arrive at 4 smaller rectangles. The whole rectangle area is S. Let the lower right small rectangle area be X.
S = 2*3+2*5+2*4-X = 6+10+8-X
On the other hand, the lower right small rectangle is proportional to other areas in this way:
X/10 = 8/S
Solve to get: X=4, S=20
The shaded area is thus S-3-5-4=8.