📚 Mastering Mensuration: Area, Volume and Surface Area for IGCSE | 掌握度量几何：IGCSE 中的面积、体积与表面积
Mensuration is a core topic in IGCSE Mathematics. It involves measuring lengths, areas, volumes and surface areas of two-dimensional (2D) and three-dimensional (3D) shapes. You will meet these skills in Papers 2 and 4, often combined with real-world problems.
度量几何是 IGCSE 数学的核心专题。它涉及测量二维图形和三维物体的长度、面积、体积以及表面积。你会在 Paper 2 和 Paper 4 中遇到这些技能，并且常常与实际应用问题相结合。
1. What is Mensuration? | 什么是度量几何？
Mensuration is the branch of mathematics that deals with the measurement of geometric figures. In IGCSE, you must understand four key ideas: perimeter, area, volume and surface area.
度量几何是研究几何图形测量的数学分支。在 IGCSE 中，你需要理解四个关键概念：周长、面积、体积和表面积。
Perimeter is the total distance around a 2D shape.
周长是二维图形周围的总距离。
Area is the amount of space inside a 2D shape, measured in square units.
面积是二维图形内部的区域大小，用平方单位表示。
Volume is the space occupied by a 3D object, measured in cubic units.
体积是三维物体所占的空间，用立方单位表示。
Surface area is the total area of all faces of a 3D object.
表面积是三维物体所有面的总面积。
These measurements appear in everyday life, such as calculating the amount of paint needed for a wall or the capacity of a water tank. A solid grasp of formulae and unit conversions is essential.
这些测量出现在日常生活中，例如计算粉刷一面墙所需的油漆量或水箱的容量。因此，扎实掌握公式和单位换算至关重要。
2. Units and Conversions | 单位与换算
Always check units before starting a calculation. For length, the standard conversions use powers of 10. For area and volume, the conversion factors are squared or cubed.
在开始计算前，一定要检查单位。长度使用 10 的幂进行换算，而面积和体积则需要使用平方或立方后的换算因子。
1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
1 厘米 = 10 毫米，1 米 = 100 厘米，1 千米 = 1000 米。
1 cm² = 100 mm², 1 m² = 10,000 cm².
1 平方厘米 = 100 平方毫米，1 平方米 = 10,000 平方厘米。
1 m³ = 1,000,000 cm³, and 1 litre = 1000 cm³.
1 立方米 = 1,000,000 立方厘米，且 1 升 = 1000 立方厘米。
When you calculate area or volume, write the correct power in the unit, such as cm² or m³. Convert all measurements to the same unit before substituting into a formula.
在计算面积或体积时，请在单位中写出正确的幂次，例如 cm² 或 m³。在代入公式前，先把所有测量值换算成同一单位。
3. Perimeter and Area of Basic Shapes | 基本图形的周长与面积
You must be able to recall and apply the area and perimeter formulae for rectangles, triangles, parallelograms, trapeziums and circles.
你必须能够回忆并运用矩形、三角形、平行四边形、梯形和圆的面积与周长公式。
For a rectangle with length l and width w:
A = l × w, P = 2(l + w)
对于长为 l、宽为 w 的矩形：面积 A = l × w，周长 P = 2(l + w)。
For a triangle with
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