The squares are shown in the attached picture.
As you can see, JC is half the diagonal of ABCD and JH is half the diagonal of EFGH.
In order to find the area of the shaded figure, we need to subtract the area of the white square (EFGH) from the area of the big square (ABCD).
The area of a square know the diagonal is given by the formula:
A = d² ÷ 2
A(ABCD) = (2×JC)² ÷ 2
= (2×9)² ÷ 2
= 162 cm²
A(EFGH) = (2×JH)² ÷ 2
= (2×4)² ÷ 2
= 32 cm²
Therefore:
A = A(ABCD) - A(EFGH)
= 162 - 32
= 130 cm²
The area of the shaded region is 130 cm².