Question

Find the area of the following polygon, if $AL=10cm,AM=20cm,AN=50cm,AO=60cm$ and $AD=90cm.$

Answer 1

$AL=10cm$, $AM=20cm$, $AN=50cm$, $AO=60cm$, $AD=90cm$

$LN=AN-AL=40cm$

$MO=AO-AM=40cm$

$OD=AD-AO=30cm$

$ND=AD-AN=40cm$

Area of polygon $=$ Area of ${\Delta }^{\prime \prime }AFM+\square FMDE+{\Delta }^{\prime \prime }FOD+{\Delta }^{\prime \prime }ALB+\square LBCO+{\Delta }^{\prime \prime }NCD$

$=\frac{1}{2}\times 20\times 20+\frac{1}{2}\times 40(20+60)+\frac{1}{2}\times 30\times 60+\frac{1}{2}\times 10\times 30+\frac{1}{2}\left(40\right)(30+40)+\frac{1}{20}\times 40\times 40$

$=200+1600+900+150+1400+800$

$=5050{cm}^2$