Gọi MP ∩ NQ = {O}
Ta có :
\(S_{MNPQ}=S_{MON}+S_{NOP}+S_{POQ}+S_{QOM}\)
\(\Rightarrow S_{MNPQ}=\frac{1}{2}OM.ON+\frac{1}{2}ON.OP+\frac{1}{2}OP.OQ+\frac{1}{2}OQ.OM\)
\(\Rightarrow S_{MNPQ}=\frac{1}{2}OM\left(ON+OQ\right)+\frac{1}{2}OP\left(ON+OQ\right)\)
\(\Rightarrow S_{MNPQ}=\frac{1}{2}OM.NQ+\frac{1}{2}OP.NQ\)
\(\Rightarrow S_{MNPQ}=\frac{1}{2}NQ\left(OM+OP\right)\)
\(\Rightarrow S_{MNPQ}=\frac{1}{2}NQ.MP\)
\(\Rightarrow S_{MNPQ}=\frac{18.24}{2}=216\left(cm^2\right)\)
Vậy diện tích tứ giác MNPQ là 216 cm2
