CAT 2023 Geometry & Mensuration — Previous Year Question

ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that $BC < AD$. P is a point on $AD$ such that $\triangle CPD$ is an equilateral triangle. Q is a point on $BC$ such that $AQ$ is parallel to $PC$. If the area of triangle $CPD$ is $4\sqrt{3}$, find the area of triangle $ABQ$.