Let each side of small squares be k:

Area of rectangle region = $$6k\cdot 8k=1\Rightarrow k^2=\frac{1}{6\cdot 8}$$

Therefore, area of shaded region = $$7k\cdot 5k=7\cdot 5\cdot k^2=\frac{7\cdot 5}{8\cdot 6}$$