The new side length is $ s + 4 = 14 $ cm. Compute the new area:
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- rac{\sqrt{3}}{4}s^2 = 25\sqrt{3}
- Divide both sides by $ \sqrt{3} $:
- rac{1}{4}s^2 = 25 \Rightarrow s^2 = 100 \Rightarrow s = 10 ext{ cm}
- A_{ ext{new}} = rac{\sqrt{3}}{4}(14)^2 = rac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} ext{ cm}^2
- \Delta A = 49\sqrt{3} - 25\sqrt{3} = 24\sqrt{3} ext{ cm}^2
- Thus, the area increases by $ oxed{24\sqrt{3}} $ cm².
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