The area of the parallelogram ABCD is $90 c m^{2}$ , $E C = F D$ . Find $A (Δ B E F)$ .

45 c m^{2}

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55 c m^{2}

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65 c m^{2}

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75 c m^{2}

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Solution

The correct option is A $45 c m^{2}$
$G i v e n - A B C D i s a p a r a l l e l o g r a m w i t h a r e a = {90 c m}^{2} . E C = D F . Δ B E F s h a r e s b a s e E F o n t h e l i n e F C w i t h t h e p a r a l l e l o g r a m A B C D . A l s o t h e y a r e w i t h i n t h e s a m e p a r a l l e l s A B & F C . T o f i n d o u t a r Δ B E F . S o l u t i o n - W e h a v e E C = D F ∴ E C + D E = D E + D F ⟹ E F = D C i . e T h e b a s e E F o f Δ B E F a n d b a s e D C o f p a r a l l e l o g r a m A B C D a r e e q u a l . A l s o t h e y a r e w i t h i n t h e s a m e p a r a l l e l s A B & F C . ∴ a r B E F = \frac{1}{2} a r A B C D ⟹ a r B E F = \frac{1}{2} \times {90 c m}^{2} = {45 c m}^{2} A n s - a r B E F = {45 c m}^{2}$

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Question 3
The area of the parallelogram ABCD is $90 c m^{2}$ .
Find
a) ar (ABEF)
b) ar ( $Δ$ ABD)
c) ar ( $Δ$ BEF)

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