Ta có : MN // BC
=> \(\frac{AM}{MB}=\frac{AN}{NC}\) hay \(\frac{10}{MB}=\frac{12}{6}\)
=> MB = 5
=> AB = AM + MB = 10 + 5 = 15
AC = AN + NC = 12 + 6 = 18
\(\Delta ABC\) : \(\widehat{B}=90^o\)
=> AB2 + BC2 = AC2 ( Định lý Py - ta - go )
=> BC2 = AC2 - AB2 = 182 - 152 = 99
=> BC = \(3\sqrt{11}\)
MN // BC
=> \(\frac{MN}{BC}=\frac{AN}{NC}\) hay \(\frac{MN}{3\sqrt{11}}=\frac{12}{6}\)
=> MN = \(6\sqrt{11}\)
=> \(S_{MNCB}=\frac{\left(MN+BC\right)MB}{2}=\frac{\left(6\sqrt{11}+3\sqrt{11}\right)5}{2}=\frac{45\sqrt{11}}{2}\)
