Question

Show that area(∆AHF)=area(Pentagon ABCDE).​

Answer 1

Answer:

ar(∆AHF)=ar(∆ACD) + ar(∆AHC) + ar(∆ADF)

ar(ABCDE)=ar(∆ACD) + ar(∆ABC) +

ar(∆AED)

It is given that BH parallel AC and AD parallel EF.

So,we can say ar(∆ABC)=ar(∆AHC) and ar(∆AED)=ar(∆ADF).

Now we can write ar(∆AHC) =ar(∆ABC) and ar(∆ADF)=ar(∆AEF).

Now, both ar(∆AHF) and ar(ABCDE) are the same.

Hence, ar(∆AHF) = ar(ABCDE).

proved