If each side is decreased by 2 cm, the new side length is \( 10 \) cm. The new area \( A' \) is:
["SEO Optimized Article: Solving Geometry Problems with Algebra – Find the New Area When Each Side Decreases by 2 cm", "---", "## Understanding Area Changes in a Square: If Each Side Is Decreased by 2 cm, New Area Found", "When tackling geometry problems, one common but tricky question is: What happens to the area when each side of a square is reduced by a fixed amount?\nThis article explains step-by-step how to solve the problem “If each side is decreased by 2 cm, the new side length is 10 cm. The new area ( A' ) is:” with clear math reasoning and algebraic insight — perfect for students learning geometry, algebra, or struggling to visualize side-length changes.", "---", "### The Problem Explained", "Imagine a square with side length reduced by 2 cm, resulting in a new side length of 10 cm. We are asked to find the new area ( A' ).", "At first glance, this may seem confusing — “if the new side is 10 cm, isn’t the area just ( 10^2 = 100 ) cm²?”\nYes — but only if 10 cm is the current new side length after reduction.", "Let’s carefully unravel the logic.", "---", "### Step-by-Step Breakdown", "1. Let the original side length be ( x ) cm", "Since each side is decreased by 2 cm, the new side length becomes:\n [\n x - 2\n ]", "2. We are told the new side length is 10 cm\n Therefore:\n [\n x - 2 = 10\n ]", "3. Solve for ( x ):\n [\n x = 10 + 2 = 12 \ ext{ cm}\n ]\n So the original square had a side length of 12 cm.", "4. Calculate the original area\n [\n A = 12^2 = 144 \ ext{ cm}^2\n ]", "But the focus is on the new area after side reduction, not the original.", "5. Find the new area ( A' )\n Since the new side length is 10 cm:\n [\n A' = 10^2 = 100 \ ext{ cm}^2\n ]", "---", "### Verifying with Algebra: General Solution", "Let’s generalize to avoid confusion next time:", "- Let original side = ( x )\n- New side after decrease = ( x - 2 = 10 )\n- Solve: ( x = 12 )\n- Then new area:\n [\n A' = (x - 2)^2 = 10^2 = 100 \ ext{ cm}^2\n ]", "This confirms:\n[\n\boxed{A' = 100 \ ext{ cm}^2}\n]", "---", "### Why This Problem Matters", "Studying how changing one dimension affects area helps build foundational skills for real-world applications — from architecture and construction to graphic design and everyday measurements.", "---", "### Final Answer Quick Recap", "> If each side of a square is decreased by 2 cm, resulting in a new side length of 10 cm, the new area ( A' ) is\n[\n\boxed{100 \ ext{ cm}^2}\n]", "---", "### SEO Phrases You’ll See in This Content:\n- resizing square area\n- algebra geometry problem solution\n- how to find new area after side decrease\n- side length reduction word problem\n- calculate new area given reduced measure\n- step-by-step area change calculation\n- math problem explanation with real numbers", "---", "Key Takeaway: Always trace back from the new dimension to original values before computing changes — clarity in algebra leads to accurate geometry results.", "---", "Got more geometry questions? Visit our full library on area and perimeter equations, or comment below with your next problem!", "---", "Keywords: area of square, side length decrease, algebra geometry, new area formula, math problem solve, decrease side length, 10 cm area, problem-solving geometry", "---", "Meta Description:\nDiscover how to find the new area when each side of a square is reduced by 2 cm. Step-by-step solution with algebra, validated calculations, and tips for mastering area changes in squares. Perfect for students and math learners."]
