Find area of this.polygon

Find area of this.polygon the Rillow•ing pob.ns. (iv) 6 cm 12 cm

Join : EF and DG From the figure, AB=CF=8 cm. AC=BF=2 cmNow, CE=6 cm. So, EF=CF-CE=8-6=2 cmSo, area of rectangle ABCF=length×breadth=AB×AC=8×2=16 cm2Now HI=DJ=8 cmand GJ=6 cm. So DG=DJ-GJ=8-6=2 cmand DH=JI=2 cmSo, area of rectangle DJHI=length×breadth=HI×JI=8×2=16 cm2Now calculating the area of  DGEF.Join FJ. Clearly FJ=BI-BF-JI=9-2-2=9-4=5 cmConsider rt. FGJ, by pythagoras theorem , we haveFG2=FJ2+GJ2=52+62=25+36=61So, FG=61Also, DE=FG and is parallel .and DG=EF=2 cmSo, area of EFDG=DG×DE=2×61=261 cm2So, area of polygon=area of rectangle ABCF+So, area of rectangle DJHI+area of EFDG=16+16+261 cm2=32+261 cm2=216+61  cm2

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