Let’s denote the length of XA as x and the length of CY as y.

Since AX and CY are heights of the parallelogram ABCD, we can use the formula for the area of a parallelogram: area = base * height.

The base of the parallelogram is AB, which is given as 9 cm.

The height of the parallelogram can be calculated using the formula: height = area / base.

Given that the area is 45/4 cm², we can substitute these values into the formula to find the height:

height = (45/4) / 9 = 45/36 = 5/4 cm.

Now, let’s consider the right triangle AXB. We can use the Pythagorean theorem to find the length of XA:

XA² = AB² - AX².

Substituting the known values, we have:

x² = 9² - (5/4)².

x² = 81 - 25/16.

x² = (81*16 - 25) / 16.

x² = (1296 - 25) / 16.

x² = 1271 / 16.

x = √(1271 / 16).

Similarly, let’s consider the right triangle CYB. We can use the Pythagorean theorem to find the length of CY:

CY² = CB² - CY².

Substituting the known values, we have:

y² = 5² - (5/4)².

y² = 25 - 25/16.

y² = (400 - 25) / 16.

y² = 375 / 16.

y = √(375 / 16).

Therefore, the length of XA is √(1271 / 16) cm and the length of CY is √(375 / 16) cm.