# The area of the parallelogram PQRS is 50 cm 2 . Find the distance between the parallel sides PQ and SR, if the length of the side PQ is 6 cm.

area of the parallelogram = base * vertical height

let us draw a perpendicular R to PQ, let it intersect extended PQ at M.

RM is the distance between the parallel sides PQ and SR. area of PQRS=PQ*RM=6*RM=50

therefore RM=50/6=25/3  cm.=8.33 cm.

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the area of the parellogram is b x h

so let 6 cm be either base or height according to your diagram

(well here i will take base)

so ,

area of parallelogram = B X H

50 cm2 = 6 x h

h = 50/6 cm

h= 8.34 cm

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Let us draw a diagonal SQ of parallelogram PQRS and a perpendicular SX on the extended line PQ as shown in the figure. here SX is drawn to find the distance between paralle side PQ and SR ... perpendicular SX is the distane between them.. .

We know that a diagonal of a parallelogram divides it into two congruent triangles. Also, congruent figures are equal in area.

∴ ar (ΔPQS) = ar (ΔQRS)

Area of parallelogram = ar (ΔPQS) + ar (ΔQRS) = 2 ar (ΔPQS)

∴ ar (ΔPQS) = 1/2 area of parallelogram=1/2*50cm2 = 25 cm2

Also, ar (ΔPQS) = 1/2 (PQ) (SX) = 25 cm2

⇒ (PQ) (SX) = 50 cm2

⇒ SX = 50cm/6(Since it is given that PQ = 6 cm)

⇒ SX = 8.34 cm

Thus, the distance between the parallel sides PQ and SR is 8.34 cm....

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