For (a + b)(a – b), remove corner square b² from square a²; rearrange the remaining L-shape into rectangle (a + b) by (a – b). For (a + b + c)², divide a square into 9 blocks yielding a² ...
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In 60 minutes, the minute hand turns 360°, so in 10 minutes it turns (360/60) x 10 = 60°. The area swept is a sector: (60/360) x (22/7) x 7² = 77/3 = 25.67 cm².
Circumference 2 x (22/7) x r = 44 yields radius r = 7 cm. A quadrant has angle 90°, so its area is (1/4) x π x r² = (1/4) x (22/7) x 7² = 77/2 = 38.5 cm².
Midpoints cut each corner triangle’s area to 1/4 of its diagonal triangle. Summing opposite corner triangles removes 1/4 + 1/4 = 1/2 of the total 4-gon area, leaving exactly half for the inner Varignon parallelogram.
Diagonal PR divides parallelogram PQRS into equal triangles PSR and PQR. Similarly, triangles OSR and OQR share base and equal heights, making their areas equal. Subtracting gives area(ΔPSO) = area(ΔPQO).