Calculate: \( SA = 2(20 + 24 + 30) = 2 \times 74 =
["# How to Calculate the Sum of Areas: Understanding the Formula ( SA = 2(20 + 24 + 30) = 2 \ imes 74 = 148 )", "When tasked with calculating the surface area of a three-dimensional shape, simple arithmetic often becomes essential—especially in geometry and engineering applications. One common scenario involves summing the areas of all planar faces and multiplying by a constant factor, such as 2 for metallic or panel surfaces. This article explains how to calculate surface area using the formula ( SA = 2(S_1 + S_2 + S_3) ), using your example: ( SA = 2(20 + 24 + 30) = 2 \ imes 74 = 148 ).", "## What Is Surface Area?", "Surface area (SA) measures the total area of all the exterior surfaces of a 3D object. Whether you're designing a box, calculating material needs for a construction, or solving a geometry problem, accurate surface area computation is critical.", "## The Formula Explained", "For polyhedra made of flat polygonal faces, the standard surface area formula is:", "[\nSA = 2 \ imes (\ ext{Sum of areas of all individual faces})\n]", "Here, multiplying by 2 accounts for both sides of the surface—important when accounting for coatings, paint, or material thickness on both inner and outer layers.", "## Applying the Formula Step-by-Step", "Let’s break down your example:", "Step 1: Add the areas of individual faces", "Given:\n( S_1 = 20 ), ( S_2 = 24 ), ( S_3 = 30 )", "[\nS_1 + S_2 + S_3 = 20 + 24 + 30 = 74\n]", "Step 2: Multiply the sum by 2", "[\nSA = 2 \ imes 74 = 148\n]", "## Why Multiply by 2?", "If the object is solid into which a thin layer of material (like paint or metal) must be applied on both sides, multiplying by 2 ensures full coverage:", "[\n\ ext{Total surface area} = 2 \ imes (\ ext{sum of face areas})\n]", "### Practical Applications:", "- Packaging and Filling: Calculating the total material needed for a box with labeled side areas.\n- Manufacturing: Estimating raw material prices based on total surface area.\n- Education: Teaching students core geometry and unit conversion concepts.", "## Example Summary", "Using the surface area formula:", "[\nSA = 2(20 + 24 + 30) = 2 \ imes 74 = 148\n]", "The total surface area is 148 square units.", "## Conclusion", "Calculating surface area with ( SA = 2(20 + 24 + 30) = 148 ) is straightforward once you understand the concept of summing face areas and accounting for both sides. This principle underlies countless real-world calculations—making it a vital skill in STEM disciplines.", "---", "If you found this guide helpful, explore more geometry tutorials and practice problems to strengthen your mathematical foundation!"]
