CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

CAT Questions | CAT Mensuration Questions | Triangle

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:-
CAT : Geometry: Mensuration; Triangle
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.


CAT Preparation Online | CAT Geometry - Mensuration Videos On YouTube

Other useful sources for Geometry Questions | Mensuration Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now