CAT Practice : Mensuration

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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. ${\frac {1}{√2}}$ cm2

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 = ${\frac {1}{2}}$ x PO x OT = ${\frac {1}{2}}$ x ${\frac {2√2}{2}}$(PO = ${\frac {2√2}{2}}$ as diagonal of square = √2a) x (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 = 1 cm2

=) A ∆ POT = √2 +1 - 1 = √2 cm2

Choice (C) is therefore, the correct answer.

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Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.