Surface area is \(2(lw + lh + wh) = 2(4 \times 5 + 4 \times 6 + 5 \times 6) = 2(20 + 24 + 30) = 148\) square centimeters.
["Understanding Surface Area: Calculating Surface Area of a Rectangular Prism (With Example)", "When studying geometry, one of the fundamental concepts is the surface area of 3D shapes—it’s the total area covering the surface. For a rectangular prism, surface area helps describe how much material is needed to cover its entire shape, like packaging boxes, manufacturing containers, or designing buildings.", "In this article, we’ll explore how to calculate the surface area using the standard formula and walk through a real-world calculation: finding the surface area of a rectangular prism with dimensions 4 cm, 5 cm, and 6 cm.", "---", "### What is Surface Area of a Rectangular Prism?", "The surface area ( S ) of a rectangular prism with length ( l ), width ( w ), and height ( h ) is given by the formula:", "[\nS = 2(lw + lh + wh)\n]", "This formula accounts for all six faces: each pair of opposite faces contributes twice the area of a rectangle.", "---", "### Why Does This Formula Work?", "A rectangular prism has:", "- Two faces of size ( l \ imes w ) (top and bottom)\n- Two faces of size ( l \ imes h ) (front and back)\n- Two faces of size ( w \ imes h ) (sides)", "Summing all face areas and multiplying by 2 gives the total surface area:", "[\nS = 2(lw + lh + wh)\n]", "---", "### Step-by-Step Calculation Example", "Let’s apply the formula using actual measurements:\nLet ( l = 4 ) cm, ( w = 5 ) cm, ( h = 6 ) cm.", "1. Calculate each pairwise product\n [\n lw = 4 \ imes 5 = 20 \ ext{ cm}²\n ]\n [\n lh = 4 \ imes 6 = 24 \ ext{ cm}²\n ]\n [\n wh = 5 \ imes 6 = 30 \ ext{ cm}²\n ]", "2. Add them together\n [\n lw + lh + wh = 20 + 24 + 30 = 74 \ ext{ cm}²\n ]", "3. Multiply by 2 to get total surface area\n [\n S = 2 \ imes 74 = 148 \ ext{ cm}²\n ]", "---", "### Final Result", "Therefore, the surface area of the rectangular prism with dimensions 4 cm × 5 cm × 6 cm is 148 square centimeters:", "[\n\boxed{2(4 \ imes 5 + 4 \ imes 6 + 5 \ imes 6) = 2(20 + 24 + 30) = 148 \ ext{ cm}^2}\n]", "---", "### Practical Applications of Surface Area Calculations", "- Packaging design: Minimizing material use while maximizing space.\n- Thermal management: Estimating heat transfer on surfaces.\n- Construction and manufacturing: Quantifying paint or coating required.\n- Education: Teaching geometric concepts in math and science curricula.", "Understanding how to calculate surface area empowers students, engineers, and professionals to make informed decisions based on real-world spatial measurements.", "---", "### Summary", "- The formula for surface area of a rectangular prism is ( 2(lw + lh + wh) ).\n- Each term represents the area of opposite faces.\n- Plugging in values like 4 cm, 5 cm, and 6 cm gives a surface area of 148 cm².\n- Accurate surface area calculations support planning across industries.", "Whether you're a student solving geometry problems or a professional calculating material needs, mastering surface area formulas is essential for precision and efficiency.", "---", "Keywords: surface area formula, rectangular prism surface area, calculate surface area, geometry example, 2(lw + lh + wh), surface area calculation, 4 × 5 × 6, educational geometry, packaging math.\nMeta Description: Learn how to calculate the surface area of a rectangular prism using the formula 2(lw + lh + wh). Example: 4×5×6 cm gives 148 cm² surface area. Ideal for students and educators."]
