CAT 2018 Slot 1 QA Question 31: 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 triangl

Question

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 triangl

Accepted Answer

Since AP is perpendicular to CD, AP is the height corresponding to base CD of the parallelogram.
$CD 	imes AP = 72$
$9 	imes AP = 72$
$AP = 8$
In right triangle APD, $AD = 16$ and $AP = 8$.
$DP = \sqrt{AD^{2} - AP^{2}} = \sqrt{16^{2} - 8^{2}}$
$DP = \sqrt{192} = 8\sqrt{3}$
Area of triangle APD is

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