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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? 📰 Taco Johns Secrets Unfold The Menu Thats Turning Hunger Into Craving 8577977 📰 Werehog Sonic Unleashed The All Star Boss Battle Thats Taking Over Gaming 307326 📰 Deque In Java 3467292 📰 Chicken Mole Recipe 5302711 📰 Rent A Tesla 4679997 📰 Amanda Nunes Next Fight 8154295 📰 What Time Does The College Championship Game Come On Tonight 7994222 📰 Master Pivot Tables Today Your Go To Guide To Creating Excel Pivot Tables Like A Guru 7973756 📰 Www Wells Fargo Online Banking Sign In 9314086 📰 The Ultimate Ggll Stock Secret How This Name Shockingly Dominated The Market Today 3072565 📰 Finally Revealed How The Judas Contract Manipulates Your Mind Dont Look Away 2075951 📰 Microsoft Edge View2 Runtime Leak See How It Boosts Speed But Has Hidden Risks 4092743 📰 Whats Triggering The Dow Jones Drop Expert Breakdown Inside The Numbers 5645712 📰 Popcorn Time For Mac 1809930 📰 From Chaos To Clarity The Month Day Year Format That Every Planner Swears By 3797542