A rectangular prism has dimensions 4 cm by 5 cm by 6 cm. What is the surface area?
["Understanding the Surface Area of a Rectangular Prism: A Simple Guide with Dimensions 4 cm × 5 cm × 6 cm", "When studying geometry, understanding the surface area of three-dimensional shapes is essential—especially rectangular prisms. Many students and learners ask: What is the surface area of a rectangular prism with dimensions 4 cm, 5 cm, and 6 cm? In this article, we’ll break down the formula, explain each step clearly, and show you how to calculate the surface area step by step.", "### What Is a Rectangular Prism?", "A rectangular prism is a 3D shape with six rectangular faces, where all angles are right angles (90°). Common examples include boxes, tables, and bricks. For dimensions 4 cm × 5 cm × 6 cm, one face measures 4 cm × 5 cm, another 5 cm × 6 cm, and the third 4 cm × 6 cm.", "### What Is Surface Area?", "Surface area refers to the total area of all the outer surfaces of a 3D object—the amount of 2D space the shape occupies on its outer surface. Since a rectangular prism has six faces, each a rectangle, we calculate the area of each face individually and then sum them.", "### 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\n- ( w ) = width\n- ( h ) = height", "### Plugging in the Values", "For dimensions:\n- ( l = 6 ) cm\n- ( w = 5 ) cm\n- ( h = 4 ) cm", "Now substitute these values:", "1. Calculate each pair:\n - ( lw = 6 \ imes 5 = 30 , \ ext{cm}^2 )\n - ( lh = 6 \ imes 4 = 24 , \ ext{cm}^2 )\n - ( wh = 5 \ imes 4 = 20 , \ ext{cm}^2 )", "2. Sum the products:\n [\n lw + lh + wh = 30 + 24 + 20 = 74 , \ ext{cm}^2\n ]", "3. Multiply by 2:\n [\n SA = 2 \ imes 74 = 148 , \ ext{cm}^2\n ]", "### Conclusion", "The surface area of a rectangular prism with dimensions 4 cm × 5 cm × 6 cm is 148 square centimeters.", "Understanding this formula helps in real-world applications like packaging design, construction, and even everyday tasks involving containers and boxes. Whether you're a student, teacher, or DIY enthusiast, mastering surface area calculations brings clarity and precision to geometry.", "If you’re looking to visualize or solve similar problems, consider drawing the prism, labeling each face, and applying the formula systematically. Practice strengthens accuracy—so grab a ruler and a calculator, and try calculating surface areas for different dimensions.", "---", "Keywords: rectangular prism surface area, surface area formula, geometric calculations, 4 cm × 5 cm × 6 cm, mathematics guide, 3D geometry, surface area of a rectangular prism, how to calculate surface area, geometry lesson, math tutorial."]
