A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion...

Question

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 m^2 is ___________.

A. 1.43  B. 2.06  C. 2.68  D. 2.88

Accepted Answer

Total area = (1 + sqrt(3)/4) * 1.44 approximately 2.06 m^2 The window has a square base topped by an equilateral triangle whose base is the top side of the square. The 'perimeter' of the window traces the outside boundary: it goes around 3 sides of the square (bottom and two sides) and then the two slant sides of the equilateral triangle (the shared top side of the square is interior, not on the perimeter). With side length s: perimeter = 3s + 2s = 5s = 6, so s = 1.2 m. Then total area = s^2 + (sqrt(3)/4)*s^2.