PQRTS is a Pentagon. A line through T meets QR in U such that ...

PQRTS is a Pentagon. A line through T meets QR prouduced in U such that SR || UT. Show that ar(PSUQ)=ar(PQRTS)

Answer

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Q -PQRTS is a pentagon A line Through t meels ar (PSUQ) = ar (PQRTS)

 Q R U

 X S T

In fig, ∆ STR and ∆ RTS are on the same base RS and between parallel lines RS ∥ VT (given)

               ∴ ar (∆ STR) = ar (∆ RTS)      …….(1)

         Now, ar (PSVQ) = ar (PSRQ) + ar (∆ STR)

                                   = ar (PSRQ) + ar (∆RTS)

               (From (1))

             ar (PQRTS)

    ∴ ar (PSVQ) = ar (PQRTS)