Textbook Problem

Suppose that the lateral faces of the pyramid in Exercise 5 have $A_{ABE}=12i{n}^2$, $A_{BCE}=16i{n}^2$, $A_{CDE}=12i{n}^2$, and $A_{DAE}=10i{n}^2$. If each side of the square base measures $4in.$, find the total surface area of the pyramid.