Question

Answer 1

ΔMNP vuông tại N

=>\(MP^2=MN^2+NP^2\)

=>\(MP^2=6^2+6^2=72\)

=>\(MP=6\sqrt{2}\left(cm\right)\)

ΔQMP cân tại Q

=>\(\widehat{QMP}=\widehat{QPM}=\dfrac{180^0-46^0}{2}=\dfrac{134^0}{2}=67^0\)

Xét ΔQMP có \(\dfrac{PM}{sinQ}=\dfrac{QM}{sinQPM}\)

=>\(\dfrac{QM}{sin67}=\dfrac{6\sqrt{2}}{sin46}\)

=>\(QM\simeq10,86\left(cm\right)\)

\(S_{MQP}=\dfrac{1}{2}\cdot MQ\cdot MP\cdot sinQMP\)

\(=\dfrac{1}{2}\cdot10,86\cdot6\sqrt{2}\cdot sin67\simeq42,4\left(cm^2\right)\)

\(S_{MNP}=\dfrac{1}{2}\cdot6\cdot6=6\cdot3=18\left(cm^2\right)\)

\(S_{MNPQ}=S_{QMP}+S_{MNP}=42,4+18=60,4\left(cm^2\right)\)