ABCD and EFGH are squares. If JH= 4cm and JC=9cm, then what is the area of the shaded region?

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.