Given that ABCD is a rectangle.AB=10cm,BC=6cm.P,Q,R,S are mid points of sides AB,BC,CD,DA.Find area of quadrilateral PQRS. (hint:- first prove that ar (pqrs)=1/2ar(abcd). I KNOW THE ANSWER i.e.30 cm BUT I NEED THE EXPLNATION
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join SQ and PR mark the intersecting point as O.
now SQ=10cm {because AB=10cm and AB is parallel to SQ}
similarly,
PO=3cm[because BQ=6m and half of that is 3cm]
now quadrilateral PQRS=ar of PSQ and SRQ
area of PSQ=1/2bh where b=10cm[SQ] and h=3cm[PO]
therefore area of PSQ=15cm
similarly area of SRQ=15CM
THEREFORE area of quadrilateral PQRS=15+15=30cm
now SQ=10cm {because AB=10cm and AB is parallel to SQ}
similarly,
PO=3cm[because BQ=6m and half of that is 3cm]
now quadrilateral PQRS=ar of PSQ and SRQ
area of PSQ=1/2bh where b=10cm[SQ] and h=3cm[PO]
therefore area of PSQ=15cm
similarly area of SRQ=15CM
THEREFORE area of quadrilateral PQRS=15+15=30cm
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