First we find the length (L) of a large rectangle:
[tex]L= \frac{20x^2+49x+30}{4x+5} =\frac{20x^2+25x+24x+30}{4x+5} =\frac{5x(4x+5)+6(4x+5)}{4x+5} = \\ \\ = \frac{(4x+5)(5x+6)}{4x+5} =5x+6[/tex]
Now find the length (l) of the smaller (shaded) rectangle:
[tex]l=5x+6-5x=6 \ in[/tex]
So, the area of the shaded region = 6 * 5 = 30 in².
