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Home » If each side is increased by \(2\) cm, the new side length becomes: - AMAZONAWS

If each side is increased by \(2\) cm, the new side length becomes: - AMAZONAWS

📅 March 11, 2026 👤 scraface

Mar 11, 2026

$If each side is increased by \(2\) cm, the new side length becomes:$

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

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