Each circle of diameter d sits in a square cell of area d². The ratio of circle area to each cell is (π / 4)d² / d² = π / 4. Both figures have covered fraction π / 4 approximately ...
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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.
Drawing a diagonal splits the trapezium into two triangles having bases a and b, each sharing perpendicular height h. Summing their areas gives (1/2)ah + (1/2)bh = (1/2)(a + b)h.
Circumference 2 x (22/7) x r = 66 gives radius r = 21/2 cm. The area of the quadrant is (1/4) x π x r² = (1/4) x (22/7) x (21/2)² = 693/8 = 86.625 cm².
Wheel circumference is π x d = (22/7) x 60 = 1320/7 cm (approx 1.886 m). For 100 rotations, total distance is 100 x (1320/7) = 132000/7 cm ≈ 18857.14 cm = 188.57 m.