Answer:
5/9 of the area of square ABCD is shaded
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
To find out what fraction of the area of square ABCD is shaded, divide the shaded area by the total area of square ABCD
step 1
Find out the area of square ABCD
The area of a square is
[tex]A=b^{2}[/tex]
where
b is the length side of the square
we have
[tex]b=(x+2x)=3x\ units[/tex]
so
[tex]A=(3x)^{2}[/tex]
[tex]A=9x^2\ units^{2}[/tex]
step 2
Find out the area of the 4 congruent right triangles
[tex]A=4[\frac{1}{2}(x)(2x)]=4x^{2}\ units^2[/tex]
step 3
Find out the area of the shaded region
The area of the shaded region is equal to the area of square ABCD minus the area of the 4 congruent right triangles
so
[tex]A=9x^2-4x^{2}=5x^{2}\ units^{2}[/tex]
step 4
Divide the shaded area by the total area of square ABCD
[tex]\frac{5x^{2}}{9x^{2}} =\frac{5}{9}[/tex]
therefore
5/9 of the area of square ABCD is shaded
