LetÂ ADÂ be the perpendicular dropped fromÂ AÂ to the sideÂ BCÂ andÂ PSÂ be the perpendicular dropped fromÂ PÂ to the sideÂ QRÂ respectively.
Since,Â Î”ABCâˆ¼Î”PQR, we haveÂ Î”ABDâˆ¼Î”PQS.
Therefore,
AB/PQâ€‹=AD/PSâ€‹=BC/QRâ€‹ â‡’arÎ”ABCâ€‹/arÎ”PQR=ADÃ—BCâ€‹/PSÃ—QR =AB/PQâ€‹Ã—AB/PQ =AB^2â€‹/PQ^2 =1/9â€‹

LetÂ ADÂ be the perpendicular dropped fromÂ AÂ to the sideÂ BCÂ andÂ PSÂ be the perpendicular dropped fromÂ PÂ to the sideÂ QRÂ respectively.

Since,Â Î”ABCâˆ¼Î”PQR, we haveÂ Î”ABDâˆ¼Î”PQS.

Therefore,

AB/PQâ€‹=AD/PSâ€‹=BC/QRâ€‹

â‡’arÎ”ABCâ€‹/arÎ”PQR=ADÃ—BCâ€‹/PSÃ—QR

=AB/PQâ€‹Ã—AB/PQ

=AB^2â€‹/PQ^2

=1/9â€‹