A rectangular prism has dimensions 4 cm, 5 cm, and 6 cm. What is its surface area?
["Understanding the Surface Area of a Rectangular Prism: A 4 cm × 5 cm × 6 cm Example", "When studying geometry, one essential concept is the surface area of three-dimensional shapes. A rectangular prism is a fundamental solid with six rectangular faces, each pair opposite and equal in area. Today, we’ll explore how to calculate the surface area of a rectangular prism with dimensions 4 cm, 5 cm, and 6 cm—showcasing a practical application that’s valuable in math education, architecture, engineering, and everyday problem-solving.", "---", "### What Is a Rectangular Prism?", "A rectangular prism is a three-dimensional shape with all faces being rectangles. It has three pairs of parallel rectangular faces, and its dimensions are defined by its length (l), width (w), and height (h). In our example, the dimensions are 4 cm (length), 5 cm (width), and 6 cm (height).", "---", "### 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- l = length = 6 cm\n- w = width = 5 cm\n- h = height = 4 cm", "Plugging in the values:", "[\nSA = 2 \left( (6 \ imes 5) + (6 \ imes 4) + (5 \ imes 4) \right)\n]", "[\nSA = 2 \left( 30 + 24 + 20 \right)\n]", "[\nSA = 2 \ imes 74 = 148 , \ ext{cm}^2\n]", "---", "### Why This Formula Works", "A rectangular prism has six faces: two of each type—length × width, length × height, and width × height. The total surface area is the sum of the areas of all these faces. The formula efficiently combines these areas using multiplication and doubling for opposite faces.", "---", "### Real-World Applications", "Knowing the surface area of a rectangular prism is essential in many fields:", "- Packaging Design: Calculating how much material is needed to construct a box.\n- Construction: Estimating paint or wallpaper required for rectangular structures.\n- Classroom Learning: Teaching spatial reasoning and geometric principles.\n- Manufacturing: Optimizing production materials and minimizing waste.", "---", "### Conclusion", "Calculating the surface area of a rectangular prism like one with dimensions 4 cm × 5 cm × 6 cm involves a clear, straightforward formula that highlights the shape’s geometry. In this case, the surface area measures 148 cm². Understanding such calculations not only reinforces foundational math skills but also empowers practical problem-solving across various disciplines.", "Whether you’re a student, educator, or a DIY enthusiast, mastering surface area calculations for rectangular prisms opens doors to clearer spatial thinking and better design decisions.", "---", "Key Takeaway:\nFor a rectangular prism with dimensions length = 6 cm, width = 5 cm, and height = 4 cm, the surface area is 148 cm² (calculated as ( 2(6×5 + 6×4 + 5×4) = 148 )).", "Keywords: rectangular prism surface area, surface area formula, geometry 4x5x6 cm, calculate rectangular prism area, math education, volume and surface area tutorial."]
