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Home » Or sum 224 for n=14. - ClickBalance

Or sum 224 for n=14. - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 The side length \(s\) of the original equilateral triangle is:

📌 s = \frac{18}{3} = 6 \text{ cm}

📌 The area \(A_1\) of an equilateral triangle with side \(s\) is:

📌 A_1 = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} \text{ square cm}

📌 If each side is increased by 2 cm, the new side length is \(8\) cm. The new area \(A_2\) is:

📌 A_2 = \frac{\sqrt{3}}{4} \times 8^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3} \text{ square cm}

📌 A_2 - A_1 = 16\sqrt{3} - 9\sqrt{3} = 7\sqrt{3} \text{ square cm}

📌 Thus, the area increases by \(\boxed{7\sqrt{3}}\) square cm.

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