# CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

###### CAT Questions | CAT Mensuration Questions | Squares
CAT Questions

This question is from CAT Mensuration in CAT Geometry.In this question, a square is drawn inside a square with some given conditions and it is repeated for infinite times and we need to find the sum of all squares. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam. Combo of Mensuration and Geometric Progressions make for an interesting question.

Question 13: ABCD is a square drawn inside a square PQRS of sides 4 cm by joining midpoints of the sides PQ, QR, RS, SP. Another square is drawn inside ABCD similarly. This process is repeated infinite number of times. Find the sum of all the squares.

1. 16 cm2
2. 28 cm2
3. 32 cm2
4. Infinite

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##### Method of solving this CAT Question from Geometry - Mensuration: Let's go with the given details.

Diagram -

AP = PB = 2cm
∴ AB = √(22 + 22) = √8 = 2√2 cm

Similarly, BE = EH = $$frac{2√2}{2}\\$ = √2 cm ∴ EH = √$√22 + √22)
= √4 = 2 cm
If we write the infinite series of area of squares,
= 42 + (2√2)2 + 22 + ……. infinite
Since it is a decreasing series sum of infinite terms can be approximated.
= 16+8+4+………infinite
∴ a (first term) = 16 , r = $$frac{1}{2}\\$$in the infinite G.P)
Sum of an infinite G.P = $$frac{a}{1 - r}\\$ = $\frac{16}{1-1/2}\\$ = 32 cm2 The question is " Find the sum of all the squares. " ##### Hence, the answer is 32 cm2 Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Geometry - Mensuration Videos On YouTube #### Other useful sources for Geometry Questions | Mensuration Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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