The area of the parallelogram ABCD is $90 c m^{2}$ (see Fig.9.13) EC=FD. Find $A (A B E F)$

45 c m^{2}

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60 c m^{2}

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90 c m^{2}

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180 c m^{2}

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Solution

The correct option is C $90 c m^{2}$
$G i v e n - A B C D i s a p a r a l l e l o g r a m w h o s e a r e a = 90 {c m}^{2} . A B E F i s a n o t h e r q u a d r i l a t e r a l w i t h t h e s a m e b a s e A B a n d w i t h i n t h e s a m e p a r a l l e s A B & F C w i t h t h e p a r a l l e l o g r a m A B C D . E C = D F . T o f i n d o u t - a r A B E F . S o l u t i o n - E C = F D ∴ E C + D E = F D + D E ⟹ D C = E F = A B ∴ A B E F i s a l s o a p a r a l l e l o g r a m A l s o A B C D & A B E F h a v e t h e s a m e b a s e A B a n d a r e w i t h i n t h e s a m e p a r a l l e s A B & F C . ∴ a r A B E F = a r A B C D = {90 c m}^{2} A n s - a r A B E F = {90 c m}^{2}$

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