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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 9 cm. The area of the parallelogram is given as 45/4 cm². So we have:

(45/4) = 9 * x

Simplifying this equation, we get:

45 = 36x

Dividing both sides by 36, we find:

x = 45/36 = 5/4 cm

So the length of XA is 5/4 cm.

Now let’s consider the height CY. Since AX and CY are heights of the parallelogram, they are parallel to each other. Therefore, the length of CY is equal to the length of AB, which is 9 cm.

So the length of CY is 9 cm.

In summary, the length of XA is 5/4 cm and the length of CY is 9 cm.