CAT Practice : Mensuration

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Mensuration  Question 5
Another beautiful question.

Area of Triangle

    Q.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. cm2

 

  • Correct Answer
    Choice C. √2 cm2

Detailed Solution

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 ---------- (1)

A ∆POT = x PO x OT = x (PO = as diagonal of square = √2a) x (OS + ST)

= * ( + 2)

= 1 *

= √2+1

A∆ POS = * Area of square

= * 22 = 1 cm2

=) A ∆ POT = √2 +1 - 1 = √2 cm2

Choice (C) is therefore, the correct answer.

Correct Answer: √2 cm2



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Mensuration

  1. Cone and Frustum
  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.