PQRS is parallelogram with diagonals PR and QS intersecting at a point E. if area of traingle SEP + area of triangle QER = 12 sq.cm,nfind the area of paralleogram PQRS
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We have a parallelogram PQRS with diagonal PR and QS intersecting at a point E.
We know from properties of parallelogram that the diagonals of parallelogram bisect each other so,
ar(∆SEP) = ar(∆QER) = ar(∆SER) = ar(∆PEQ)
ar(∆SEP) = ar(∆QER) = ar(∆SER) = ar(∆PEQ) = 1/4ar(PQRS)
⇒ (ar(∆SEP) + ar(∆QER)) = 1/2ar(PQRS)
So,
1/2ar(PQRS) = 12
⇒ar(PQRS) = 12*2
⇒ ar(PQRS) = 24 cm^2
We know from properties of parallelogram that the diagonals of parallelogram bisect each other so,
ar(∆SEP) = ar(∆QER) = ar(∆SER) = ar(∆PEQ)
ar(∆SEP) = ar(∆QER) = ar(∆SER) = ar(∆PEQ) = 1/4ar(PQRS)
⇒ (ar(∆SEP) + ar(∆QER)) = 1/2ar(PQRS)
So,
1/2ar(PQRS) = 12
⇒ar(PQRS) = 12*2
⇒ ar(PQRS) = 24 cm^2
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