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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Polygons : In a parallelogram ABCD of area 72 sq cm . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:
Q. 3: In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is?
As given, Area of parallelogram ABCD = 72
AP = 8 cm
in right-angled triangle APD, AP^2 + PD^2 = AD^2
So PD^2 = AD^2-AP^2 = 16^2-8^2 = 64×3
Thus Area of triangle APD = 1/2 AP×PD = 1/2×8×8√3 = 32√3