Area of a trapezium

Question

Given the following trapezium: Where area of the triangle BCP is equal to 12 and $|DC|=7$, $|AB|=28$ Calculate the area of a trapezium. How to do that? as it seems that there are no sufficient data to calculate the desired area.

Answer 1

HINT :

Since $\triangle{CDP}$ and $\triangle{ABP}$ are similar, we have $$CP:AP=CD:AB=7:28=1:4.$$ Also, we have $$[\triangle{CPB}]:[\triangle{APB}]=CP:AP=1:4.$$

Note also that $[\triangle{CPB}]=[\triangle{DPA}]$. (why?)