Bài giải:

AM = 2 MB; BN = 2 NC; CP = 2 PA

Ta có $BN=\frac{2}{3}BC$ $\Rightarrow $ $S\vartriangle MBN=\frac{2}{3}S\vartriangle MBC$

Mà $BM=\frac{1}{3}AB$ $\Rightarrow $ $S\vartriangle BMC=\frac{1}{3}S\vartriangle ABC$

Suy ra $S\vartriangle MBN=\frac{2}{3}.\frac{1}{3}S\vartriangle ABC=\frac{2}{9}S\vartriangle ABC$

Tương tự ta chứng minh được :

$S\vartriangle BMN=S\vartriangle PNC=S\vartriangle AMP=\frac{2}{9}S\vartriangle ABC$

Suy ra $S\vartriangle MNP=\left( 1-3.\frac{2}{9} \right)S\vartriangle ABC=\frac{1}{3}S\vartriangle ABC$

Vậy $S\vartriangle MNP=\frac{1}{3}.360=120$ (cm2)