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

📚 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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