Three congruent isosceles triangles DAO, AOB, and OBC have AD=AO=OB=BC=10 and AB=DO=OC=12. These triangles are arranged to form trapezoid ABCD, as shown. Point P is on side AB so that OP is perpendicular to AB.
Point X is the midpoint of AD and point Y is the midpoint of BC. When X and Y are joined, the trapezoid is divided into two smaller trapezoids. The ratio of the area of trapezoid ABYX to the area of trapezoid XYCD in simplified form is p:q. Find p+q.