A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 12 cm. What is the surface area of the prism?
["Understanding the Surface Area of a Rectangular Prism: A 8 cm × 5 cm × 12 cm Example", "When studying geometry, one key concept students often encounter is the surface area of a rectangular prism. Understanding how to calculate this helps in real-world applications like packaging, construction, and design. In this article, we’ll explore how to compute the surface area of a rectangular prism with dimensions: 8 cm in length, 5 cm in width, and 12 cm in height.", "### What Is a Rectangular Prism?", "A rectangular prism is a three-dimensional shape with six rectangular faces, opposite faces being equal. It has three dimensions: length (L), width (W), and height (H). In our example:\n- Length (L) = 8 cm\n- Width (W) = 5 cm\n- Height (H) = 12 cm", "Each face contributes to the total surface area, so calculating surface area involves adding up the areas of all six rectangular sides.", "### Formula for Surface Area", "The surface area ( SA ) of a rectangular prism is calculated using this formula:", "[\nSA = 2(LW + LH + WH)\n]", "Where:\n- ( LW ) = area of the front/back face\n- ( LH ) = area of the left/right face\n- ( WH ) = area of the top/bottom face", "### Step-by-Step Calculation", "Substituting our values into the formula:", "1. Calculate each pair of face areas:\n - Front/back: ( L \ imes W = 8 \ imes 5 = 40 , \ ext{cm}² )\n - Left/right: ( L \ imes H = 8 \ imes 12 = 96 , \ ext{cm}² )\n - Top/bottom: ( W \ imes H = 5 \ imes 12 = 60 , \ ext{cm}² )", "2. Plug into the surface area formula:\n[\nSA = 2(40 + 96 + 60) = 2(196) = 392 , \ ext{cm}²\n]", "### Final Answer", "The surface area of a rectangular prism with a length of 8 cm, width of 5 cm, and height of 12 cm is 392 square centimeters.", "### Why Knowing Surface Area Matters", "Knowing surface area is essential for practical tasks such as determining how much paint or material is needed to cover a box, how much fabric to produce a wrapped gift, or estimating heat transfer in science applications. Mastering this concept builds a strong foundation in geometry and geometry-based problem solving.", "---", "Incorporate this formula and method into your studies to confidently calculate surface areas for any rectangular prism. If you found this guide helpful, share it to help others master geometric calculations!"]
