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Q.

State true or false.

If in the given figure, O is any point inside a parallelogram ABCD, then

$a r (△ O A D) + ar(△ O B C) = ar(parallelogram ABCD)$ .

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a

True

b

False

answer is B.

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Detailed Solution

It is given that O is any point inside the parallelogram ABCD.
Question Image

Question Image

We have to check if ar(

ΔOAD)

+ar(

ΔOBC)

=ar(Parallelogram ABCD)
When a triangle and parallelogram are aligned on the same base and between the same parallel lines, then the area of the triangle is equal to half of the area of the parallelogram.
Considering a parallelogram and constructing PQ||AB, RS||AD as depicted in the figure below.
Question Image

Question Image

Considering ∆OAD and parallelogram ABQP shown in the figure. They have the same base AB and lie between parallel lines AB and PQ.
Area of ∆OAD

= 12 Area of parallelogram ABQP ...... (i)

Area of ∆OBC

= 12 Area of parallelogram PQCD ..... (ii)

Adding equations (i) and (ii),
Area of ∆OAD+ Area of ∆OBC

= 12 Area of parallelogram ABQP + 12 Area of parallelogram PQCD = 12 (Area of parallelogram ABQP + Area of parallelogram PQCD) = 12 Area of parallelogram ABCD

S o, A r e a of △ O A D + Area of △ O B C = 12 Area of parallelogram ABCD

Thus, the statement is false.
Therefore, option 2 is correct.

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