Question

Find the area of polygon if AC=95cm, AH=85 cm, AF= 10cm, EF=45cm, DH=55cm and BG=40 cm.

Answer 1

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Question



Find the area of pentagon ABCDE in which BL⊥AC,CM⊥AD and EN⊥AD such that AC=10cm,AD=12cm,BL=3cm,CM=7cm and EN=5cm.





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Solution



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Area of pentagon ABCDE= Area of ΔABC+Area of ΔACD+ Area of ΔADE

Here , BL⊥AC,CM⊥AD,EN⊥AD

So, BL, CM and EN perpendiculars to ΔABC,ΔACD and  ΔADE respectively.

Area of triangle with perpendicular =1/2×base×height

∴ Area of ΔABC=1/2×AC×BL

Area of ΔACD=1/2×AD×CM

Area of ΔADE=1/2×AD×EN

Now area of pentagon ABCDE=1/2AC×BL+1/2×AD×CM+1/2×AD×EN

=(1/2×10×3)+(1/2×12×7)+(1/2×12×5)

=15+42+30

=87