Four top rectangles match five bottom ones in length, giving 4l = 5b, so l = 5b/4. Area 9lb = 72 yields lb = 8. Solving gives b = 2.53 cm, l = 3.16 cm, and perimeter ā 11.38 cm.
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Let OA = OB = r. Semicircle on diameter AB has radius r/ā2 and area (1/4)ĻrĀ². Subtracting circular segment AFB from both the semicircle and the quarter circle OAB leaves equal areas for both shaded regions.
Let the rectangle have dimensions X and Y. The vertical dividing line of height h gives C = (1/2)hxā. Combining expressions A + C = (1/2)hX and B + C = (1/2)xāY 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 unitsĀ².
For Fig. 6.43, sides are divided into halves and thirds; subtracting unshaded triangles leaves 7/18 of the total area. For Fig. 6.44, midpoints of the square sides produce the classic inner square of area 1/5.