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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? 📰 2025S Hottest Uas Strategy Secrets You Need To Try Before Summer Invades 9298441 📰 Shafts Side Quest The Untold Story Behind This Gripping Action Thriller 8054527 📰 Game Game Ps Vita 9066474 📰 Diesel Or V8 The Truth About The Pontiac Trans Ams Radical Transformation 5883527 📰 What Is An Erp System The Simple Definition You Need To Know Today 4131264 📰 Auto Loan Financing 2419975 📰 Mcd Island 3448250 📰 Fox 4 News Kansas City 1676476 📰 Step By Step 529 Account Tutorial You Need To Watch Before Tax Season 3443848 📰 Unleash Your Hearthstone Win Potential With The Best Deck Tracker For Windows Gaming Secret Revealed 5863028 📰 All Dti Codes Revealed The Hidden Secrets That Will Change How You Work 1336959 📰 Unlock The Secret To Radiant Joydiscover Your Sunshine Mindset Tonight 3116116 📰 Words With X On The End 6794463 📰 People Are Obsessed With This Cursed Emojiis It B Judgement Or A Hidden Warning 5203865 📰 Shocking Boba Flavors Thatll Make Your Taste Buds Dance 7724693