Answer:
The fraction of the area of ACIG represented by the shaped region is 7/18
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
In the square ABED find the length side of the square
we know that
AB=BE=ED=AD
The area of s square is

where b is the length side of the square
we have

substitute


therefore

step 2
Find the area of ACIG
The area of rectangle ACIG is equal to

substitute the given values

step 3
Find the area of shaded rectangle DEHG
The area of rectangle DEHG is equal to

we have


substitute

step 4
Find the area of shaded rectangle BCFE
The area of rectangle BCFE is equal to

we have


substitute

step 5
sum the shaded areas

step 6
Divide the area of of the shaded region by the area of ACIG

Simplify
Divide by 5 both numerator and denominator

therefore
The fraction of the area of ACIG represented by the shaped region is 7/18