A rectangular prism has dimensions 4 cm by 5 cm by 6 cm. What is its surface area?
["What Is the Surface Area of a Rectangular Prism with Dimensions 4 cm × 5 cm × 6 cm?", "Understanding the surface area of a three-dimensional shape is essential in many real-world applications, from engineering and architecture to packaging and manufacturing. One common object studied in geometry is the rectangular prism—a shape defined by six rectangular faces, length, width, and height. If you’re wondering “What is the surface area of a rectangular prism that measures 4 cm by 5 cm by 6 cm?”—this article breaks it down clearly and precisely.", "---", "### What Is a Rectangular Prism?", "A rectangular prism is a polyhedron with eight rectangular faces, twelve edges, and six vertices. It’s a 3D shape where all angles are right angles, and opposite faces are identical rectangles. Common examples include cardboard boxes, bricks, and many storage containers.", "---", "### The Formula for Surface Area", "The surface area (SA) of a rectangular prism is calculated using the formula:\n[\nSA = 2(lw + lh + wh)\n]\nWhere:\n- ( l ) = length (6 cm)\n- ( w ) = width (5 cm)\n- ( h ) = height (4 cm)", "This formula accounts for all six faces:\n- Two faces of size ( l \ imes w )\n- Two faces of size ( h \ imes w )\n- Two faces of size ( h \ imes l )", "---", "### Step-by-Step Calculation", "Plugging the dimensions into the formula:", "[\nSA = 2[(6 \ imes 5) + (6 \ imes 4) + (5 \ imes 4)]\n]", "First, compute each product inside the brackets:\n- ( 6 \ imes 5 = 30 )\n- ( 6 \ imes 4 = 24 )\n- ( 5 \ imes 4 = 20 )", "Add them:\n[\n30 + 24 + 20 = 74\n]", "Now multiply by 2:\n[\nSA = 2 \ imes 74 = 148 , \ ext{cm}^2\n]", "---", "### Final Answer", "The surface area of a rectangular prism with dimensions 4 cm × 5 cm × 6 cm is 148 square centimeters.", "---", "### Why Surface Area Matters", "Knowing the surface area helps in:\n- Estimating material needs for construction or crafting\n- Calculating heat transfer in thermally sensitive applications\n- Ensuring proper fit and sealing in packaging design", "This simple rectangular prism calculation is a foundational concept in geometry and engineering—showing how math models real-life objects with precision.", "---", "Keywords: Rectangular prism surface area, calculate surface area, 4 cm × 5 cm × 6 cm, geometry formula, surface area calculation, 3D shapes, educational math, dimensional math."]
