# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Mensuration Questions | Question 29

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Question 29 :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

1. 18√3
2. 24√3
3. 32√3
4. 12√3

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##### Method of solving this CAT Question from Mensuration

Given Area (ABCD) = 72 sq cm, CD = 9cms, AD = 16cms
Area of Parallelogram = Base × Height
CD × 16 = 72
CD = $$frac{72}{16}$ cms We extend CD till P such that ∠APD = 90° So, again by applying the area formula considering CD as base CD × AP = Area of Parallelogram ABCD 9 × AP = 72 AP = 8 cms We have AP = 8 cms, AD = 16 cms We observe that the ratio of the sides form a 1 : √3 : 2 triangle Therefore DP = 8√3 cms Area$△APD) = 1/2 × AD × DP = 1/2 × 8 × 8√3 sq cms Area (△APD) = 32 √3 sq cms

The question 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 "

##### Hence, the answer is 32√3 sq cms

Choice C is the correct answer.

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