Quantitative Aptitude – Geometry – Polygons – In a parallelogram ABCD of area 72 sq cm

Quantitative Aptitude – Geometry - Polygons – In a parallelogram ABCD of area 72 sq cm

Slot -1 – Quantitative Aptitude – Geometry – Polygons – In a parallelogram ABCD of area 72 sq cm

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?

a) 24√3

b) 12√3

c) 32√3

d) 18√3

Answer: c) 32√3

Solution:

As given, Area of parallelogram ABCD = 72
So AB×AP=72

9AP=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

PD=8√3
Thus Area of triangle APD = 1/2 AP×PD = 1/2×8×8√3 = 32√3

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