Scaling linear dimensions by factor k increases area by k²: 2² = 4 and 3² = 9. Yes, in each case exactly 4 or 9 congruent copies tile and perfectly fit into the scaled figure without gaps.
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Inverting a second congruent trapezium alongside the first forms a parallelogram of base (a + b) and height h. Its area is (a + b)h, so one trapezium has area (1/2)(a + b)h.
One complete turn equals circumference 2 x (22/7) x 28 = 176 cm = 1.76 m. For 1 km (100,000 cm), turns = 100000 / 176 = 568.18, which is approximately 568 full turns.
Sides are 2x, 3x, 4x with sum 9x = 45, giving sides 10 cm, 15 cm, 20 cm. Semi-perimeter s = 22.5 cm. By Heron’s formula, area = √(22.5 x 12.5 x 7.5 x 2.5) = (75/4)√15 cm² (approx 72.62 ...
Inscribed equilateral triangle side is a = r√3. Triangle area is (√3/4) x a² = (√3/4) x 3r² = (3√3/4)r². Dividing by circle area πr² yields ratio (3√3) / (4π) ≈ 0.413.