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Home » 5a + b = 7 \quad \text(Equation 5) - Portal da AcÃºstica

5a + b = 7 \quad \text(Equation 5) - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \frac{1}{4} s^2 = 36 \quad \Rightarrow \quad s^2 = 144 \quad \Rightarrow \quad s = 12 \text{ cm}

📌 The new side length is:

📌 s' = 12 + 2 = 14 \text{ cm}

📌 A' = \frac{\sqrt{3}}{4} (14)^2 = \frac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} \text{ cm}^2

📌 \Delta A = A' - A = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3} \text{ cm}^2

📌 Thus, the area increases by \(\boxed{13\sqrt{3}}\) square centimeters.Question: Find the area enclosed by the graph of $ |x| + |y| = 4 $.

📌 Solution: The equation $ |x| + |y| = 4 $ describes a diamond (or rhombus) centered at the origin. To find the vertices, consider the four cases for absolute values:

📌 $ x \geq 0, y \geq 0 $: $ x + y = 4 $, intercepts at $ (4, 0) $, $ (0, 4) $

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