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📰 \]Question: An anthropologist discovers ancient carvings depicting a regular hexagon with an area of \( 54\sqrt{3} \) square units. If each side is reduced by 2 units, by how many square units does the area decrease? 📰 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? 📰 Fine Hotels 8022833 📰 54 Alarming Bad Omens Merch Revealed Is Your Space Haunted By These Spooky Goods 6550984 📰 Aulani Disney Hotel And Resort Hawaii 2722663 📰 The Ultimate Farm Games Compilation You Need To Play This Weekshocking Hidden Gems Inside 6780759 📰 Unbelievable Ice Cube War Of The World Begins Preparing For The Ultimate Freeze 2400329 📰 Gmail Out Of Office 3650492 📰 Wells Fargo Bank Hastings Nebraska 2208348 📰 Pastel Dresses 4173426 📰 Can Your Oracle Sql Queries Survive Without If Statements Find Out Now 7637795 📰 Applebees All You Can Eat 9798267 📰 Physicians Npi Lookup 2887433 📰 Hilum Renalis 1102641 📰 Musify Mp3 Downloader 9433771 📰 The Lost Secrets Of Levantu Hollow They Wont Tell You 2801785 📰 King Charles Terminally Ill 7508504