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In the figure ABCD is a quadrilateral in which diagonal BD = 64 cm, AL $⊥$ BD and CM $⊥$ BD such that AL = 16.8 cm and CM = 13.2 cm. The area of the quadrilateral ABCD is:

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920

c m 2

930

c m 2

960

c m 2

980

c m 2

answer is C.

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Detailed Solution

Given ABCD is a quadrilateral in which diagonal BD = 64 cm, AL

⊥

BD and CM

⊥

BD such that AL = 16.8 cm and CM = 13.2 cm.
In the given figure, ABCD is a quadrilateral in which diagonal BD=64;cm, AL⟂ BD and CM⟂BD such that AL=16.8;cm and CM=13.2;cm. Calculate the area of the quadrilateral ABCD. | Snapsolve

In the given figure, ABCD is a quadrilateral in which diagonal BD=64;cm, AL⟂ BD and CM⟂BD such that AL=16.8;cm and CM=13.2;cm. Calculate the area of the quadrilateral ABCD. | Snapsolve

A r e a o f Δ A B D

is,

A r e a o f Δ A B D = 12 × b a s e × h e i g h t ⇒ A r e a o f Δ A B D = 12 × B D × A L ⇒ A r e a o f Δ A B D = 12 × 64 × 16.8 ⇒ A r e a o f Δ A B D = 537.6 c m 2

Now,

A r e a o f Δ B C D

is,

A r e a o f Δ B C D = 12 × b a s e × h e i g h t ⇒ A r e a o f Δ B C D = 12 × B D × C M ⇒ A r e a o f Δ B C D = 12 × 64 × 13.2 ⇒ A r e a o f Δ B C D = 422.4 c m 2

Area of quadrilateral ABCD is,
Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

⇒

Area of quadrilateral ABCD = 537.6 + 422.2

⇒

Area of quadrilateral ABCD = 960

c m 2

Hence, option 3 is correct.

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