∴ Quadrilateral CFGE is a rectangle

∴CG=EF,CF=GE

BG=BE-GE=BE-CF

∴S quadrilateral ABCD

=S△ABE+S rectangular CFGE+S△BCG+S△CDF

= 1/2ae×BE+ef×CF+ 1/2cg×BG+ 1/2df×CF

= 1/2ae×BE+EF×CF+ 1/2(BE-CF)×EF+ 1/2df×CF

= 1/2ae×BE+ef×CF+ 1/2ef×BE- 1/2ef×CF+ 1/2df×CF

= 1/2ae×BE+ 1/2ef×BE+ 1/2ef×CF+ 1/2df×CF

= 1/2be×(AE+EF)+ 1/2cf×(EF+DF)

= 1/2BE×AF+ 1/2CF×ED

= 1/2×8× 12+ 1/2×6× 10

=48+30

=78 square centimeters