Given,

A trapezium, ABCD in which AB‖DC, P and Q are Points on AD and BC respectively,

Such that PQ || DC.

Thus,

AB||PQ||DC.

In ∆ABD,

PO || AB [∵ PQ || AB]

By basic proportionality theorem,

If a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, the other two sides are divided in the same ratio.

By basic proportionality theorem,

From equation (i) and (ii)

→ AP = 42

∴ AD = AP + DP

AD = 42 + 18 = 60

So, AD = 60 cm