# CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

###### CAT Questions | CAT Mensuration Questions | Triangle CAT Questions

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 9 full classes for free The Best CAT Online Coaching Courses ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sun, March 1st, 2020 ### 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. ###### Signup and sample 9 full classes for free The Best Online CAT Coaching Courses. Signup ! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sun, March 1st 2020 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ## 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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