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
[tex]A=b^{2}[/tex]
where b is the length side of the square
we have
[tex]A=49\ units^2[/tex]
substitute
[tex]49=b^{2}[/tex]
[tex]b=7\ units[/tex]
therefore
[tex]AB=BE=ED=AD=7\ units[/tex]
step 2
Find the area of ACIG
The area of rectangle ACIG is equal to
[tex]A=(AC)(AG)[/tex]
substitute the given values
[tex]A=(9)(10)=90\ units^2[/tex]
step 3
Find the area of shaded rectangle DEHG
The area of rectangle DEHG is equal to
[tex]A=(DE)(DG)[/tex]
we have
[tex]DE=7\ units[/tex]
[tex]DG=AG-AD=9-7=2\ units[/tex]
substitute
[tex]A=(7)(2)=14\ units^2[/tex]
step 4
Find the area of shaded rectangle BCFE
The area of rectangle BCFE is equal to
[tex]A=(EF)(CF)[/tex]
we have
[tex]EF=AC-AB=10-7=3\ units[/tex]
[tex]CF=BE=7\ units[/tex]
substitute
[tex]A=(3)(7)=21\ units^2[/tex]
step 5
sum the shaded areas
[tex]14+21=35\ units^2[/tex]
step 6
Divide the area of of the shaded region by the area of ACIG
[tex]\frac{35}{90}[/tex]
Simplify
Divide by 5 both numerator and denominator
[tex]\frac{7}{18}[/tex]
therefore
The fraction of the area of ACIG represented by the shaped region is 7/18
