Question

Find the area of pentagon ABCDE in
which BLI AC, CM I AD and EN I AD
such that AC = 8 cm AD =12
BL=4 cm, CM=6 cm and EN=5 cm

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Answer 1

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Answer 2

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

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