Consider, pls, this solution:
1) the area of the figure may be imagined as sum of areas of 3 figures:
S=S₁+S₂+S₃, where S₁ - area of ABF; S₂ - area of ABCD and S₃ - area of CDE.
2) S₁=S₃=0.5*2*7=7 units², S₂=AB*BC=7*4=28 units².
3) S=7+7+28=42 units².
For more details see the attached picture.