Question

An agriculture field has a shape of an irregular polygon as shown in the figure. It's dimensions are given. Calculate it's area.

Given:$AB=220m,AL=20m,AM=30m,BN=160m,OB=40m,TM=OS=60m,LP=20m,NQ=60m,MN=30m$

Answer 1

To find the area of the field we need to find the sum of area of its parts.

Area of $△ALP=\frac{1}{2}\times AL\times LP$

$=\frac{1}{2}\times 20\times 20=200{\text{m}}^2$

Area of trapezium $PLNQ=\frac{1}{2}\times LN\times (LP+NQ)$

$=\frac{1}{2}\times 40\times (20+60)$

$=\frac{1}{2}\times 40\times 80=1600{\text{m}}^2$

Area of ractangle $QNBR=BN\times NQ=160\times 60=9600{\text{m}}^2$

Area of $△AMT=\frac{1}{2}\times AM\times MT=\frac{1}{2}\times 30\times 60=900{\text{m}}^2$

Area of rectangle $TMOS=TM\times OM=60\times 150=9000{\text{m}}^2$

Area of $△SOB=\frac{1}{2}\times OS\times OB=\frac{1}{2}\times 60\times 80=1200{\text{m}}^2$

$\therefore$Area of the field$=200+1600+9600+900+9000+1200=22,500{\text{m}}^2$