Question

13. In the given figure, AB || DC || EF, AD || BE and DE || AF. Prove that :
ar( || gm DEFH) ar(|| gm ABCD).
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Answer 1

Answer:

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Step-by-step explanation:

In the given figure, we have

AB || DC and AD || BC, which implies that ABCD is a parallelogram. Similarly, we can show that ADEG and DEFH are also parallelograms.

Here, we will be using the theorem that two parallelograms standing on the same base and lying between the same pair of parallel lines have equal areas.

Now, since parallelograms ABCD and ADEG stand on the same base and lying between the same pair of parallel lines AD and BE. So, we have

Area of ABCD = Area of ADEG.

Again, since parallelograms ADEG and DEFH stand on the same base DE and lying between the same pair of parallel lines DE and AF. So, we have

Area of ADEG = Area of DEFH.

Thus, we arrive at

Area of ABCD = Area of DEFH.

Hence proved.