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Area of Trapezium by Finding the Area of a Triangle of Same Area

In Fig. 9.4, ...

Question

In Fig. 9.4, the area of parallelogram ABCD is :

A

AD x BM

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B

BC x BN

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C

DC x DL

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D

AD x DL

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Solution

The correct options are
A AD x BM
C DC x DL
$G i v e n - A B C D i s a p a r a l l e l o g r a m . D L ⊥ A B & B M ⊥ A D . T o f i n d o u t - a r A B C D . S o l u t i o n - D L ⊥ A B ∴ D L i s t h e h e i g h t o f A B C D w h e n i t s b a s e i s A B . ∴ a r A B C D = D L \times A B . . S i m i l a r l y B M ⊥ A D . ∴ B M i s t h e h e i g h t o f A B C D w h e n i t s b a s e i s A D . ∴ a r A B C D = B M \times A D A n s - O p t i o n A & C$

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