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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? 📰 Hide And Seek Extreme 📰 What Is Playing At The Movies 1862283 📰 Fid Cd Rates 📰 Love Strikes Big Taylor Swift The Bracelet Travis Kelce Has Just Confirmed His Engagement 4624520 📰 The Cut The Rope 📰 Colonist Survival Game 📰 Sabrina And The Animated Series 1401016 📰 First Plucked From A Tree Guarded By A Snake 8259211 📰 Discover The Hidden Power Of Vivian Paper In Mario Every Player Must See This 6165828 📰 Crafting A Saddle Youre Doing It Wrongthis Pro Method Will Change How You Play 9925779 📰 Delta Baggage Check In Price 📰 Amorphous Disk Mark 71919 📰 Talkie Ai App Shocked The Worldthis Revolutionary Voice To Video App Lets You Talk See Reality Live 2515997 📰 Bodhi Kosher Vegetarian Restaurant 8594133 📰 Microsoft Live Photo Gallery