CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

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

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.