In the given figure Abcd is a rectangle with length (p2q-5) and breadth (q2+4p)findthe area of shaded triangle pab - Maths - Algebraic Expressions

Question

In the given figure Abcd is a rectangle with length (p2q-5) and
breadth (q2+4p)findthe area of shaded triangle pab

Neha Sethi · Accepted Answer

Area of rectangle  ABCD =length l×breadth b=AB×BC=p2q-5×q2+4p    given length=p2q-5 and breadth=q2+4p=p2q-5q2+4p sq
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Now from the figure we can observe that △PBC is symmteric to △PADSo, area of △PBC=area of △PADAssuming P to be the mid point of CDNow we know that each angle of rectangle is 90°⇒∠C=90°Area△PBC=12×CB×PC  area of right △=12×base×height=12×q2+4p×p2q-52=q2+4pp2q-54 sq
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So, Area△PBC=Area of △PAD=q2+4pp2q-54So, area of shaded region=Area of rectangle  ABCD- Area△PBC+Area of △PAD=p2q-5q2+4p-q2+4pp2q-54+q2+4pp2q-54=p2q-5q2+4p-2q2+4pp2q-54=4q2+4pp2q-5-2q2+4pp2q-54=2q2+4pp2q-54=q2+4pp2q-52    sq
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