Take into account that the given kite can be cosidered as a rhombus.
The formula for the area of a rhombus is:
A = (d1 x d2)/2
where d1 and d2 are the diagonals of the rhombus.
In this case:
d1 = WY = 13 in
d2 = XZ = ?
A = 65 in²
solve the formula for d2 and replace the values of the other parameters to find d2, as follow:
d2 = 2A/d1
d2 = 2(65 in²)/(13 in)
d2 = 10 in
XZ = d2 = 10 in
Hence, the length of the segment XZ is 10 in