Let OA = OB = r. Semicircle on diameter AB has radius r/√2 and area (1/4)πr². Subtracting circular segment AFB from both the semicircle and the quarter circle OAB leaves equal areas for both shaded regions.
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Let the rectangle have dimensions X and Y. The vertical dividing line of height h gives C = (1/2)hx₂. Combining expressions A + C = (1/2)hX and B + C = (1/2)x₂Y yields the rectangle area XY = [2(A + ...
Semicircles have diameter 2, radius 1. Perimeter consists of 4 full semicircular arcs totaling 4 x (pi x 1) = 4pi units. Flower area equals 4 semicircles minus the square: 2pi – 4 units².
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.
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.