A square's side length is increased by 50%. If the original side length is 8 cm, calculate the percentage increase in the area.
["### Understanding the Percentage Increase in Area When a Square’s Side Length Increases by 50%", "When studying geometry, one of the most fundamental concepts is the area of a square. The area of a square is calculated using the formula:", "$$\n\ ext{Area} = \ ext{side} \ imes \ ext{side} = \ ext{side}^2\n$$", "Suppose you have a square with an original side length of 8 cm. If the side length is increased by 50%, the new side length becomes:", "$$\n8 , \ ext{cm} + 0.5 \ imes 8 , \ ext{cm} = 8 , \ ext{cm} + 4 , \ ext{cm} = 12 , \ ext{cm}\n$$", "Now, let’s calculate the area before and after the increase:", "- Original Area:\n$$\n8^2 = 64 , \ ext{cm}^2\n$$", "- New Area:\n$$\n12^2 = 144 , \ ext{cm}^2\n$$", "To find the percentage increase in area, use the formula:", "$$\n\ ext{Percentage Increase} = \left( \frac{\ ext{New Area} - \ ext{Original Area}}{\ ext{Original Area}} \right) \ imes 100\n$$", "Substitute the values:", "$$\n\ ext{Percentage Increase} = \left( \frac{144 - 64}{64} \right) \ imes 100 = \left( \frac{80}{64} \right) \ imes 100 = 1.25 \ imes 100 = 125%\n$$", "Conclusion:\nWhen each side of a square increases by 50%, the area increases by 125%. This striking rise in area—much greater than the 50% increase in side length—demonstrates how area scales quadratically with linear dimensions in two-dimensional shapes.", "Whether you're solving math problems, designing structures, or working with real-world measurements, understanding how shape transformations affect area is key. An increase of just a modest 50% in side length leads to a dramatic 125% gain in area—proving the power of geometric principles.", "---", "Keywords for SEO:\nsquare area calculation, percentage increase in area, side length increase 50%, geometry math problems, area compared to side change, geometry fundamentals, how to calculate area increase, math lesson geometry, square transformation math, area percentage increase 8cm side."]
