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Home » ight) = 2R \cdot rac{\sqrt3}2 = R\sqrt3 - Dyverse

ight) = 2R \cdot rac{\sqrt3}2 = R\sqrt3 - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 In the second: $ x + y \geq 0, x - y \leq 0 \Rightarrow 2y $

📌 In the third: $ x + y \leq 0, x - y \leq 0 \Rightarrow -2x $

📌 In the fourth: $ x + y \leq 0, x - y \geq 0 \Rightarrow -2y $

📌 $ 2|x| \leq 8 \Rightarrow |x| \leq 4 $

📌 $ 2|y| \leq 8 \Rightarrow |y| \leq 4 $

📌 Thus, the region is a square with side length 4, bounded by $ |x| \leq 4 $, $ |y| \leq 4 $, and symmetric across both axes.

📌 This is a square centered at the origin with vertices at $ (\pm4, 0), (0, \pm4) $. The area is:

📌 \text{Area} = \frac{1}{2} \cdot \text{diagonal}_1 \cdot \text{diagonal}_2 = \frac{1}{2} \cdot 8 \cdot 8 = 32

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