# CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

###### CAT Questions | CAT Mensuration Questions | Triangle
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This question is from CAT Mensuration in CAT Geometry.In this question, the sides of a square is given and with given condition we need to find the area of the new triangle formed. 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. Its's another beautiful question that tests the understanding in properties of triangle.

Question 5: PQRS is a square of sides 2 cm & ST = 2 cm. Also, PT=RT. What is the area of ∆PST?

1. 2 cm2
2. √3 cm2
3. √2 cm2
4. $$frac{1}{√2}\\$cm2 ## 2IIM : Best Online CAT Coaching #### Signup and sample 5 classes for free ## Best CAT Coaching in Chennai #### Batches filling fast. Starts Sat, June 8th, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Geometry - Mensuration: Although the figure looks like a 3D figure but on reading through the question, it is clear that the diagram is on a single plane. Notice, ∆PST ~ ∆SRT$all three sides equal). So, TS extended will meet PR at cross points of diagonal as shown:-

Now, A ∆ PST = A ∆ POT – A ∆ POS ---------- Equation(1)
A ∆POT = $$frac{1}{2}\\$ * PO * OT = $\frac{1}{2}\\$ * $\frac{2√2}{2}\\$$PO = $$frac{2√2}{2}\\$ as diagonal of square = 2√a) *$OS + ST)
=$$frac{√2}{2}\\$ *$$$frac{2√2}{2}\\$ + 2) = 1 * $\frac{2 + √2}{√2}\\$ = √2 + 1 A ∆ POS = $\frac{1}{4}\\$ * Area of Square = $\frac{1}{4}\\$ * 22 = 1cm2 => A ∆ POT = √2 +1 - 1 = √2 cm2 The question is " What is the area of ∆PST? " ##### Hence, the answer is √2 cm2 Choice C is the correct answer. ###### Best Online CAT CoachingSignup and sample5 classes for free Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiEnroll at 29000/- Next Weekend Batch Starts Sat, June 29th, 2019 ###### Best CAT Coaching in ChennaiEarly Bird discount of 7000 Personalised attention, Small batch sizes. ## 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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