Book Maths Puzzle

ABCD is a parallelogram G is a point on AB such that AG=2GB, E is a point on DC such that CE=2DE and F is a point on BC such that BF=2FC Prove that
(i)ar(ADEG)=ar(GBCE)
(ii)ar(EGB)=1/6 ar(ABCD)
(iii) ar(EFC)=1/2 ar(EBF)
(iv) ar(EBG)=ar(EFC)

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Book Other Question

Evaluate sec^2 30 degree + cot^2 45 degree - cosec^2 60 degree cos^2 30 degree. A rectangular tank's capacity is 189 kilometers. It is 7 m long and 4.5 m high. Find its breadth.