A rectangular prism has dimensions 4 cm by 5 cm by 6 cm. Calculate its surface area.
["# Surface Area of a Rectangular Prism: A Complete Guide with Dimensions 4 cm × 5 cm × 6 cm", "When studying 3D geometry, understanding the surface area of a rectangular prism is essential. A rectangular prism, often called a cuboid, is defined by three dimensions: length, width, and height. In this article, we’ll explore how to calculate the surface area of a rectangular prism with dimensions 4 cm, 5 cm, and 6 cm, step by step.", "---", "## What is a Rectangular Prism?", "A rectangular prism is a three-dimensional shape with six rectangular faces. It has:\n- Three pairs of identical rectangular faces\n- Opposite faces parallel and equal in area\n- Angles all measuring 90 degrees", "Gaining familiarity with surface area calculations helps in real-world applications like packaging, construction, and design.", "---", "## The Formula for Surface Area", "The surface area (SA) of a rectangular prism with length ( l ), width ( w ), and height ( h ) is calculated using the formula:", "[\nSA = 2(lw + lh + wh)\n]", "This formula sums the areas of all six faces:\n- ( lw ): two faces of length × width\n- ( lh ): two faces of length × height\n- ( wh ): two faces of width × height", "---", "## Applying the Formula to Dimensions 4 cm × 5 cm × 6 cm", "Given:\n- Length ( l = 6 ) cm\n- Width ( w = 5 ) cm\n- Height ( h = 4 ) cm", "Let’s substitute these values into the surface area formula:", "[\nSA = 2[(6 \ imes 5) + (6 \ imes 4) + (5 \ imes 4)]\n]", "Calculate each product:", "- ( 6 \ imes 5 = 30 , \ ext{cm}^2 )\n- ( 6 \ imes 4 = 24 , \ ext{cm}^2 )\n- ( 5 \ imes 4 = 20 , \ ext{cm}^2 )", "Add them together:", "[\nSA = 2[(30) + (24) + (20)] = 2[74] = 148 , \ ext{cm}^2\n]", "---", "## Final Result", "The surface area of a rectangular prism with dimensions 4 cm × 5 cm × 6 cm is 148 square centimeters.", "---", "## Why This Matters", "Knowing the surface area helps in:\n- Estimating materials needed for covers or coatings\n- Calculating heat transfer rates in engineering\n- Designing storage and shipping containers efficiently", "---", "### In Summary", "| Dimension (cm) | Value |\n|----------------|-------|\n| Length ( l ) | 6 cm |\n| Width ( w ) | 5 cm |\n| Height ( h ) | 4 cm |\n| Surface Area | 148 cm² |", "Understanding and applying the surface area formula ensures accuracy in both academic work and practical applications. Whether you're a student, engineer, or DIY enthusiast, mastering this calculation is quickly essential.", "---", "Keywords: rectangular prism surface area, formula for surface area rectangular prism, calculate surface area 4 cm 5 cm 6 cm, geometry tutoring guide, workshop math – rectangular prism dimensions, 3D shape surface area, STEM learning, math problems surface area, rectangular prism calculator.", "---", "Stay sharp, calculate smart, and build a stronger foundation in 3D geometry!"]
