Let square side be s. The sum of heights to AB and CD equals s, so Area(ΔPAB) + Area(ΔPCD) = (1/2) x s x s = s²/2. Both regions equal half the square’s area, making their ratio 1:1.
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Median AD divides ΔABC into equal areas: Area(ΔABD) = Area(ΔACD). Similarly, in ΔPBC, median PD gives Area(ΔPBD) = Area(ΔPCD). Subtracting these two equations yields Area(ΔABP) = Area(ΔACP).
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.
Yes, excessive regulations can create severe supply shortages, discourage business investment and harm market efficiency. Setting prices below production costs reduces output, while complex licensing and bureaucratic hurdles burden small businesses and stifle innovative ventures.
Price controls are implemented on life-saving medicines, hand sanitisers, basic food grains and agricultural minimum support prices. Governments cap prices to prevent hoarding and exploitation, while price floors protect farmers from incurring losses.