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GATE 2016 ME (ME2) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m2 is ___________.

  1. 1.43
  2. 2.06
  3. 2.68
  4. 2.88

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Correct answer: (B) 2.06

Explanation

Let the common side be a. The shared square top and triangle base are internal, leaving three square sides and two triangle sides in the perimeter:5a=6, so a=1.2m. Area=a²+(sqrt3/4)a²=1.44(1+sqrt3/4)=2.0635m². Thus **2.06m², B**.