Question

ABCD is a parallelogram e and f are any two points on a b and BC respectively prove that area of triangle EDFequals to area of triangle DCE

Answer 1

Answer:

ar(EDF)=ar(DCE)

Step-by-step explanation:

In triangle EDF and Triangle DCE

these triangle are om same base EF and between same parallel. so ar(EDF)=ar(DCE)

Answer 2

If ABCD is a parallelogram with e and f are any two points on AB and BC respectively then the area of triangle DAF = area of triangle DCE is proved.

Step-by-step explanation:

Hi there,

There is a mistake in the question given above. I have rewritten the correct question for you and solved it accordingly. Hope this is helpful. Thanks.

Q. ABCD is a parallelogram E and F are any two points on AB and BC respectively prove that area of triangle DAF = area of triangle DCE.

Step 1:

From figure attached below, we can say that

The Δ DAF and the parallelogram ABCD have the same base AD and lie between the same parallel lines AB and CD.

We know that if a triangle and a parallelogram are on the same base and lie between the same parallel lines, then the area of the triangle is equal to half the area of the parallelogram.

∴ Area (∆ DAF) = ½ * Area (parallelogram ABCD) ……. (i)

Step 2:

Again, from the attached figure, we can say that  

The Δ DCE and the parallelogram ABCD have the same base CD and lie between the same parallel lines AD and BC.

Similarly, we get

Area (∆ DCE) = ½ * Area (parallelogram ABCD) ….. (ii)

Step 3:

Thus,

From (i) & (ii), we get

Area (∆ DAF) = Area (∆ DCE)

Hence proved

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