Project ForgeA 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 m^2 is __________.
- A1.43
- 2.06
- C2.68
- D2.88
Explanation
Let the square's side be s. The triangle's base (shared with the square's top side) is internal, not part of the perimeter, so the perimeter consists of the square's other 3 sides plus the triangle's other 2 sides: 3s + 2s = 5s = 6, giving s = 1.2 m. Area = square area + equilateral triangle area = s^2 + (sqrt(3)/4)s^2 = 1.44 x (1 + 0.433) = 1.44 x 1.433 = 2.06 m^2.
Source: GATE ME 2016 Set-2 (2016)
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