Question

3. Find the area of pentagon ABCDE in which BL I AC, DM I AC
and EN 1 AC such that AC = 18 cm , AM = 14 cm , AN = 6 cm,
BL = 4 cm, DM = 12 cm and EN = 9 cm.
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Answer 1

Answer:

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