Question
Quantitative Aptitude Question on Mensuration
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
18√3
B
24√3
C
32√3
D
12√3
Answer
32√3
Explanation
Solution
The correct answer is (C):
Area of the parallelogram ABCD = (base)(height) = (CD)(AP) = 72 sq.cm.
(CD)(AP) = 72 9(AP) = 72 ⇒ AP = 8
DP = √AD2-AP2 = √162-82 = 8√3
Area of triangle APD = 1/2 (AP)(PD) = 32√3