A rectangular prism has dimensions 4 cm, 6 cm, and 9 cm. What is the surface area of the prism?
["Understanding the Surface Area of a Rectangular Prism with Dimensions 4 cm, 6 cm, and 9 cm", "If you're studying geometry or preparing for a math test, understanding how to calculate the surface area of a rectangular prism is essential. One commonly encountered example is a prism with dimensions 4 cm, 6 cm, and 9 cm. For students and educators alike, knowing how to compute and explain the surface area helps build a strong foundation in 3D geometry.", "### What Is a Rectangular Prism?", "A rectangular prism is a 3D shape with six rectangular faces, where opposite faces are identical rectangles. These dimensions are typically represented as length (l), width (w), and height (h). In this case, the dimensions are:", "- Length = 9 cm\n- Width = 6 cm\n- Height = 4 cm", "Each pair of opposite faces contributes to the total surface area.", "### Formula for Surface Area", "The surface area (SA) of a rectangular prism is calculated using the formula:", "[\nSA = 2(lw + lh + wh)\n]", "Where:\n- ( lw ) = area of length × width\n- ( lh ) = area of length × height\n- ( wh ) = area of width × height", "### Step-by-Step Calculation", "1. Multiply length and width:\n ( 9 , \ ext{cm} \ imes 6 , \ ext{cm} = 54 , \ ext{cm}^2 )", "2. Multiply length and height:\n ( 9 , \ ext{cm} \ imes 4 , \ ext{cm} = 36 , \ ext{cm}^2 )", "3. Multiply width and height:\n ( 6 , \ ext{cm} \ imes 4 , \ ext{cm} = 24 , \ ext{cm}^2 )", "4. Sum the three products:\n ( 54 + 36 + 24 = 114 , \ ext{cm}^2 )", "5. Multiply by 2 to get total surface area:\n ( 2 \ imes 114 = 228 , \ ext{cm}^2 )", "### Final Result", "The surface area of a rectangular prism with dimensions 4 cm, 6 cm, and 9 cm is 228 square centimeters.", "### Why Surface Area Matters", "Knowing how to calculate surface area is crucial in fields like architecture, packaging design, and engineering—any discipline where material costs, heat transfer, or paint coverage depend on a shape’s outer surface. Mastering this concept helps visualize and solve real-world problems efficiently.", "---", "✅ Quick Recap:\n- Dimensions: 4 cm × 6 cm × 9 cm\n- Surface area: 228 cm²\n- Formula: ( SA = 2(lw + lh + wh) )", "Whether you're a student, teacher, or math enthusiast, calculating the surface area of a rectangular prism is a fundamental skill with wide-ranging applications."]
