Assuming unit of length to be meter...

Area of ABCD = 1×1 = 1 m^2

Area of EFGH = Area of ABCD - Area of (AEH+EBF+FCG+GDH)

Area of AEH= 1/2*AE*AH= 1/2*1/2*4/5= 1/5

Area of EBF= 1/2*EB*BF= 1/2*1/2*1/3= 1/12

Area of FCG= 1/2*FC*CG= 1/2*2/3*1/4= 1/12

Area of GDH= 1/2*GD*DH= 1/2*3/4*1/5= 3/40

Area of (AEH+EBF+FCG+GDH)= 1/5+1/12+1/12+3/40= 53/120

So, Area of EFGH= 1 - 53/120= 67/120 m^2

Note: If we devide quadrilateral EFGH into 2 triangles and use Heron's method; A=square root (s(s-a)(s-b)(s-c)), where s=(a+b+c)/2.... we get the same result.