State true or false.

In the given figure, ABDC is a quadrilateral with BE||AC and also, BE meets DC produced at E. Then area of ∆ADE=area of quadrilateral ABCD.

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True

False

answer is A.

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Detailed Solution

It is given that ABCD is a quadrilateral with BE||AC and also, BE meets DC produced at E.
Question Image

We have to check if the area of ∆ADE = area of quadrilateral ABCD.
Two or more triangles that have the same base and lie between the same parallel lines are equal in area.
Area of a triangle=

12 × base × height

Now, the area of quadrilateral ABCD,
area of ∆ACE= area of ∆ACB... (i)
Calculating by adding area of ∆ADC on both sides of equation (i), we get,
area of ∆ACE+ area of ∆ADC= area of ∆ACB + area of ∆ADC

⇒

area of ∆ADE= area of quadrilateral ABCD
Hence, area of ∆ADE= area of quadrilateral ABCD.
Thus, the statement is true.
Therefore, option 1 is correct.

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