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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}} 📰 Question: A renewable energy engineer designs a tidal turbine foundation shaped as a circular sector with radius 12 meters and central angle \( 90^\circ \). If the radius is increased by 4 meters, by how many square meters does the area increase? 📰 Solution: The area of a circular sector is \( A = \frac{\theta}{360} \pi r^2 \). Original area: \( \frac{90}{360} \pi (12)^2 = 36\pi \). New radius: \( 12 + 4 = 16 \) meters. New area: \( \frac{90}{360} \pi (16)^2 = 64\pi \). The increase is \( 64\pi - 36\pi = 28\pi \). \boxed{28\pi} 📰 You Wont Believe What A Game Changing Iterator Can Do For Your Code 1590807 📰 Soundlabs Game Changing Sound Create Bass Triggering Beats Like Never Before 7481738 📰 Viola And Agnes 794815 📰 Steph Currys Groundbreaking Under Armour Deal Thrills Fansheres What Changed Forever 1051763 📰 Fios Tv Samsung App 2657134 📰 Hidden Truth One Quarter Cup Hides More Than You Think In Every Tablespoon 8462982 📰 A Virologist Developing A Novel Antiviral Drug Discovers It Shows High Efficacy In Vitro But May Cause Severe Liver Toxicity In Animal Trials The Funding Source Pressures For Rapid Human Trials Which Ethical Principle Most Strongly Opposes Premature Human Testing 4594699 📰 Golden Frieza 2613970 📰 You Wont Believe How Ez It Is To Beat Hgss Hgss Walkthrough Guide 1003500 📰 Powerball Numbers For Wednesday September 3Rd 5916819 📰 Film Warcraft The Beginning 9184540 📰 Add Password To Excel Nowsecret Method That Works Every Time 7792534 📰 You Wont Believe How Fast 200 Meters Translates Into Feetthis Surprise Change Shocked Everyone 6179738 📰 Shocked Rocket Bot Just Automated Space Travelwatch This Tech Blow Up Now 7912547 📰 The Everything Guide To Onedrive Documentation Get Your Free Pdf Today 6027672