Q.5 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 ___________.
(A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88

The window perimeter area square equilateral triangle problem challenges students to compute the area when the perimeter is 6m. This classic geometry question features a square base topped by an equilateral triangle, with the shared side excluded from the outer perimeter.

Perimeter Calculation

Let the side length of the square (and equilateral triangle) be s meters.
The outer perimeter excludes the shared base, so it includes 3 sides from the square and 2 slanted sides from the triangle.

Thus, 5s = 6

⇒ s = 6/5 = 1.2 m

Area Calculation

Area of square: s² = (1.2)² = 1.44 m²

Area of equilateral triangle: (√3/4)s² = (1.732/4 × 1.44) ≈ 0.6235 m²

Total Area: 1.44 + 0.6235 = 2.0635 ≈ 2.06 m²

Option Analysis

• (A) 1.43: Too low; likely undercounting perimeter sides.
• (B) 2.06: Correct value based on calculation.
• (C) 2.68: Overestimate from wrong perimeter assumption.
• (D) 2.88: Likely assumes all sides counted, not excluding shared side.

Component Table

Practice this for competitive exams; the window perimeter area square equilateral triangle builds perimeter-area reasoning skills.