PB=AB-AP= 18-2x

QB=x

∴y=( 18-2x)×？ x÷2=9x-x？ (4≥x≥0)

Maximizing the area of △△PBQ is the value of maximizing Y.

∫y = 9x-x？ =(x？ -9x+20.25)+20.25

=(x-4.5)？ +20.25

When ∴x takes 4, the maximum value of y is 20.

∴△PBQ area is 20 at most.