Ta có:

S_ADM = \[\frac{1}{2}AD.\,\,DM\,\, = \,\frac{1}{2}AD.\,\,\frac{1}{2}DC\,\, = \,\,\frac{1}{4}{S_{ABCD}}\]= 12 (cm²)

S_ABN = \[\frac{1}{2}AB\,.\,\,BN\,\, = \,\,\frac{1}{2}AB.\,\,\frac{2}{3}BC\,\, = \,\,\frac{1}{3}{S_{ABCD}}\] = 16 (cm²)

S_CMN = \[\frac{1}{2}CM\,.\,\,CN\,\, = \,\frac{1}{2}\,.\,\frac{1}{2}CD.\,\,\frac{1}{3}BC\,\, = \,\,\frac{1}{{12}}{S_{ABCD}}\] = 4 (cm²)

S_AMN = 48 – 12 – 16 – 4 = 16 (cm²).