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.
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