Solution: The area \( A \) of a regular hexagon with side length \( s \) is \( A = \frac{3\sqrt3}2s^2 \). Given \( 54\sqrt3 = \frac{3\sqrt3}2s^2 \), solving for \( s^2 \) yields \( s^2 = 36 \), so \( s = 6 \). The new side length is \( 6 - 2 = 4 \). The new area is \( \frac{3\sqrt3}2(4)^2 = 24\sqrt3 \). The decrease in area is \( 54\sqrt3 - 24\sqrt3 = 30\sqrt3 \). \boxed{30\sqrt3} - IX Labs
Mar 09, 2026
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