Substituting the values, \(SA = 2(4 \times 5 + 4 \times 6 + 5 \times 6) = 2(20 + 24 + 30) = 148\) square centimeters.

["Understanding the Area Calculation: Substituting Values to Simplify (SA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6) = 148) cm²", "When solving geometric problems involving area, expressions like (SA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)) often appear in algebra-based geometry. Understanding how to substitute values into such expressions simplifies computation and enhances conceptual clarity. This SEO-optimized article explores the step-by-step substitution behind calculating the surface area of a geometric figure—commonly a composite prism or solid—using the expression (SA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)), resulting in (SA = 148) cm².", "---", "### What Is Surface Area and Why Substitution Matters?", "Surface area (SA) measures the total exposed area of a three-dimensional shape. For complex solids made of rectangle-like faces, calculating the area often involves multi-step algebraic expressions.", "The formula (SA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)) commonly arises in problems involving a composite figure composed of three rectangular faces. The coefficients (4, 5, and 6) typically represent dimensions such as length, width, or height—common in architectural sketches or mathematical models. By substituting these values into the expression, we transform abstract algebra into concrete measurements and finally into total area in square centimeters (cm²).", "---", "### Breaking Down the Expression: A Step-by-Step Substitution", "Start with the general formula:\n[\nSA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)\n]", "Step 1: Identify and substitute the dimensions\n- 4 and 5: Represent two perpendicular edges, say length and height.\n- 4 and 6: Represent length and another dimension, possibly depth.\n- 5 and 6: Represent height and breadth or another pair forming adjacent faces.", "Assign variables for clarity:\n- Let length = 4 cm\n- Let width = 6 cm\n- Let height = 5 cm", "Step 2: Substitute into the formula\nPlug the values into the expression:\n[\nSA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)\n]", "Calculate each product inside the parentheses:\n[\n4 \ imes 5 = 20 \\n4 \ imes 6 = 24 \\n5 \ imes 6 = 30\n]", "Now substitute back:\n[\nSA = 2(20 + 24 + 30)\n]", "Sum the terms inside the parentheses:\n[\n20 + 24 + 30 = 74\n]", "Multiply by 2:\n[\nSA = 2 \ imes 74 = 148\n]", "---", "### Why Is the Final Answer 148 cm²?", "The total surface area of this geometric shape—representing three rectangular faces—is 148 cm². This quantity can be interpreted in real-world applications: measuring fabric needed for construction, painting a surface, or modeling a box-shaped container. The substitution of specific dimension values into the algebraic expression bridges abstract math with practical utility, making the formula not just symbolic, but tangible.", "---", "### Practical Tips for Quick Area Calculations Using Substitution", "- Label dimensions clearly: Always define variables for length, width, and height before substituting.\n- Check units: Ensure all values are in consistent units (e.g., centimeters) to avoid dimensional errors.\n- Break down summations: Always compute inner pairs first, then sum and multiply for accuracy.\n- Use parentheses: Keep grouped terms in parentheses to avoid operator precedence issues.", "---", "### Final Thoughts", "Understanding how substitution simplifies algebraic expressions like (SA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)) empowers students and professionals alike in solving geometry problems efficiently. This form, common in solving surface areas of composite solids, highlights the power of algebra in visualizing and measuring physical spaces.", "Whether you're designing a model, studying architecture, or mastering geometry in school, mastering such substitutions helps turn complex formulas into clear, actionable results—positioning you for SEO success in search queries like “how to calculate surface area with substitution,” “step-by-step area formula substitution,” or “substituting values in surface area problems.”", "---", "Keywords for SEO:\nsurface area calculation, substitution in geometry, area formula step-by-step, Sa = 2(4×5 + 4×6 + 5×6), cm² surface area, algebra geometry problems, converting algebra to dimensions, practical surface area applications", "Meta Description:\nLearn how substituting values into (SA = 2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6)) yields 148 cm². Step-by-step guide to calculating surface area with clear algebraic substitution and practical applications."]