📚 Perimeter and Area Problem Solving | 周长与面积问题求解
Perimeter and area are two core measurement ideas in IGCSE mathematics. Perimeter measures the distance around a 2-D shape, while area measures the amount of surface inside the shape. These concepts appear throughout the Cambridge IGCSE syllabus, especially in geometry, mensuration, and word problems. This article reviews definitions, formulas, units, compound shapes, missing lengths, and common exam pitfalls.
周长和面积是 IGCSE 数学中两个核心测量概念。周长测量二维图形外边界的总长度，而面积测量图形内部表面的大小。这些概念贯穿剑桥 IGCSE 大纲，尤其是在几何、测量和应用题中。本文复习定义、公式、单位、组合图形、缺失边长以及常见考试易错点。
1. What Is Perimeter? | 什么是周长？
Perimeter is the total distance around the outside of a closed 2-D shape. To find it, add the lengths of all sides. For polygons with straight sides, this means adding every side length exactly once, without skipping any edge and without counting any interior line.
周长是闭合二维图形外边界的总长度。要求周长，需要把所有边的长度相加。对于边为直线的多边形，这意味着将每条边长恰好加一次，不遗漏任何一条边，也不计算任何内部线段。
Perimeter is always expressed in linear units such as cm, m or km, never in square units.
例如，如果一个三角形的三条边分别是 5 cm、7 cm 和 9 cm，那么它的周长是 5 + 7 + 9 = 21 cm。周长始终用长度单位表示，如 cm、m 或 km，绝不能用平方单位。
Perimeter = sum of all exterior side lengths
周长 = 所有外边长的总和
2. Perimeter of Rectangles and Squares | 矩形和正方形的周长
is very common in IGCSE questions, so you should be able to use it quickly and accurately.
矩形有两组相等的对边。如果长为 l，宽为 w，周长可以写成 P = l + w + l + w，化简后得到 P = 2(l + w)。这个公式在 IGCSE 考题中非常常见，因此你应该能够快速且准确地使用它。
Perimeter of a rectangle = 2 × (length + width)
矩形周长 = 2 × (长 + 宽)
eter is P = s + s + s + s = 4s. You can still use the rectangle formula, but 4s is faster.
正方形是四条边都相等的矩形。如果边长为 s，那么它的周长是 P = s + s + s + s = 4s。你仍然可以使用矩形周长公式，但用 4s 会更快捷。
Perimeter of a square = 4 × side
正方形周长 = 4 × 边长
3. What Is Area? | 什么是面积？
Area measures the amount of surface enclosed within a 2-D shape. It is found by counting unit squares that cover the shape without gaps or overlaps. Area is always expressed in square units, such as cm², m², or km².
面积测量二维图形内部封闭表面的大小。它可以通过数出覆盖图形且没有空隙或重叠的单位正方形来得到。面积始终用平方单位表示，如 cm²、m² 或 km²。
A = l × w. This means area is the result of two perpendicular lengths multiplied together.
对于矩形，用长乘以宽就得到每行单位正方形的个数乘以行数，因此公式是 A = l × w。这意味着面积是两条互相垂直的长度相乘的结果。
Area of a rectangle = length × width
矩形面积 = 长 × 宽
4. Area of Rectangles and Squares | 矩形和正方形的面积
4 one-metre squares fit inside the rectangle. The unit is written as m², not m, because it represents two-dimensional space.
如果一个矩形的长为 8 m，宽为 3 m，它的面积是 8 × 3 = 24 m²。这意味着有 24 个边长 1 m 的正方形可以放入该矩形内。单位写作 m²，而不是 m，因为它表示二维空间。
ifies to side × side, or s². If a square has side length 5 cm, its area is 5 × 5 = 25 cm².
正方形是一种特殊的矩形，因此它的面积公式简化为边长 × 边长，即 s²。如果一个正方形的边长为 5 cm，它的面积是 5 × 5 = 25 cm²。
