Question

Find the area of polygon $ABCDEF$, if $AD=18cm,AQ=14cm,AP=12cm,AN=8cm,AM=4cm$ and $FM,EP,QC$ and $BN$ are perpendicular to diagonal $AD$.

Answer 1

$AD=18cm,AQ=14cm,AN=8cm,AM=4cm$

$QD=AD-AQ=18cm-14cm=4cm$

$NQ=AQ-AN=14cm-8cm=6cm$

$PD=AD-AP=18cm-12cm=6cm$

$MP=AP-PM=12cm-4cm=8cm$

Area of $△AMF=\frac{1}{2}\times 5cm\times 4cm=10c{m}^2$

Area of $△EPD=\frac{1}{2}\times 6cm\times 6cm=18c{m}^2$

Area of $△QCD=\frac{1}{2}\times 4cm\times 4cm=8c{m}^2$

Area of $BCQN=\frac{1}{2}\times (5+4)cm\times 6cm=27c{m}^2$

Area of $EMFQ=\frac{1}{2}\times (5+6)cm\times 10cm=55c{m}^2$

Area of polygon $ABCDEF$=Area of $△AMF$+Area of $△EPD$+Area of $△QCD$+Area of $BCQN$+Area of $EMFQ=(10+18+8+27+55)c{m}^2=118c{m}^2$