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
where
b is the length side of the square
we have
so
step 2
Find out the area of the 4 congruent right triangles
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
step 4
Divide the shaded area by the total area of square ABCD
therefore
5/9 of the area of square ABCD is shaded