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What will be the area of quadrilateral ABCD, if it is given that BD = 16cm, AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 7cm?

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256cm2

128cm2

64cm2

None of these

answer is B.

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Detailed Solution

It is given that BD = 16cm, AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 7cm.
We have to find the area of quadrilateral ABCD.
Question Image

We know that a quadrilateral is a polygon with four edges and four vertices.
Considering the ∆ABD and ∆BCD from the figure,
Area of triangle=

12 × b a s e × h e i g h t

⇒

Area of ∆ABD =

12 × B D × A M

⇒

Area of ∆ABD= 72 cm2

⇒ Area of △ BCD= 12 × B D × C L

⇒ Area of △ BCD=56cm 2

Area of quadrilateral ABCD=

(Area of △ ABD + Area of △ BCD)

⇒

Area of quadrilateral ABCD = 72+ 56
So, area of quadrilateral ABCD =

128cm 2

.
Therefore, option 2 is correct.

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