# CAT 2018 Question Paper | Quants Slot 1

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

Beautiful question on Geometry - Mensuration at Medium level difficulty. This question that appeared in CAT 2018 Question Paper tests on the concepts of area of a parallelogram and Pythagoras theorem. Questions from Geometry are highly tested in the CAT Exam and make sure you practice this topic well during your CAT Online Preparation. If you are looking to solve more questions like these, visit 2IIM's CAT Question Bank.

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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