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Question 5 = In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.

Solution 5

                                                                                                                                                  

Answer 9 = area (∆AHF)=area (∆ACD) + area (∆AHC) + area (∆ADF)
area (ABCDE) = area (∆ACD) + area (∆ABC) + area (∆AED)
It is given that BH parallel AC and AD parallel EF.
So,we can say area (∆ABC) = area (∆AHC) and area (∆AED) = area (∆ADF).
Now we can write area (∆AHC) = area (∆ABC) and area (∆ADF) = area(∆AEF).
Now, both area (∆AHF) and area (ABCDE) are the same.
Hence, area (∆AHF) = area (ABCDE). proved