📚 Perimeter and Area: Solving Measurement Problems | 周长与面积：解决测量问题
In this lesson, we will review two important measurement ideas: perimeter and area. We will learn how to find the distance around a shape and how to measure the space inside it. Through practice, we will solve real-world problems with confidence.
在本节课中，我们将复习两个重要的测量概念：周长和面积。我们将学习如何求图形一周的长度，以及如何测量图形内部的空间大小。通过练习，我们将自信地解决生活中的实际问题。
1. What Is Perimeter? | 什么是周长？
Perimeter is the total distance around the outside of a shape. Imagine walking around the edge of a garden — the distance you walk is the perimeter.
周长是指图形外缘一周的总长度。想象你沿着花园边缘走一圈，你走过的路程就是周长。
To find the perimeter of a polygon, add all of its side lengths together.
要求多边形的周长，只需把所有边的长度加在一起。
P = side₁ + side₂ + side₃ + …
For example, a rectangle with length 5 cm and width 3 cm has perimeter P = 5 + 3 + 5 + 3 = 16 cm.
例如，一个长 5 厘米、宽 3 厘米的长方形，其周长为 P = 5 + 3 + 5 + 3 = 16 厘米。
2. Finding Perimeter of Different Shapes | 求不同图形的周长
A square has four equal sides. If one side is 4 m, the perimeter is 4 + 4 + 4 + 4 = 16 m, or 4 × 4 = 16 m.
正方形有四条相等的边。如果一条边长为 4 米，周长就是 4 + 4 + 4 + 4 = 16 米，也可以写成 4 × 4 = 16 米。
A hexagon has six sides. If each side is 2 cm, its perimeter is 2 × 6 = 12 cm.
六边形有六条边。如果每条边长 2 厘米，它的周长就是 2 × 6 = 12 厘米。
When a shape has a missing side length, use the total perimeter to find it. For example, if a rectangle has perimeter 20 cm and one side is 6 cm, the opposite side is also 6 cm, so the two remaining sides have a total length of 8 cm, which means each one is 4 cm.
当图形缺少一条边的长度时，可以利用周长来帮助求解。例如，一个长方形周长为 20 厘米，一条边为 6 厘米，对边也是 6 厘米，剩下两条边共长 8 厘米，所以每条边为 4 厘米。
3. What Is Area? | 什么是面积？
Area is the amount of space inside a two-dimensional shape. We measure area in square units, such as square centimeters (cm²) or square meters (m²).
面积是二维图形内部所占据的空间大小。我们使用平方单位来测量面积，例如平方厘米（cm²）或平方米（m²）。
Think of a sheet of paper. The entire flat surface of the paper is its area.
想象一张纸，整张纸的平整表面就是它的面积。
Area is always measured in square units because we fill the inside of shapes with unit squares.
面积总是用平方单位来度量，因为我们用单位正方形去铺满图形的内部。
4. Counting Unit Squares | 数单位正方形
One way to find area is to count how many unit squares fit inside a shape. Each unit square represents one square unit.
求面积的一种方法，是数一数图形里面可以放多少个单位正方形。每个单位正方形代表一个平方单位。
For example, a rectangle made of 2 rows with 3 squares in each row has 2 × 3 = 6 square units.
例如，一个长方形由 2 行组成，每行有 3 个小正方形，那么它就有 2 × 3 = 6 个平方单位。
This counting method helps us understand why multiplication works for finding the area of rectangles.
这种数方格的方法，帮助我们理解为什么乘法可以用于求长方形的面积。
5. Area of a Rectangle: Length × Width | 长方形的面积：长 × 宽
To find the area of a rectangle, multiply its length by its width.
要求长方形的面积，用长乘以宽。
A = l × w
For a rectangle with length 8 cm and width 5 cm, the area is A = 8 × 5 = 40 cm².
一个长 8 厘米、宽 5 厘米的长方形，面积为 A = 8 × 5 = 40 平方厘米。
A square is also a rectangle with equal sides. If one side of a square is 6 cm, its area is 6 × 6 = 36 cm².
正方形也是特殊的长方形，它的四条边都相等。如果正方形边长为 6 厘米，它的面积就是 6 × 6 = 36 平方厘米。
6. Area of Combined Rectangles | 组合图形的面积
Sometimes a shape is made of two or more rectangles put together. We can find the total area by splitting the shape into smaller rectangles, finding each area, and then adding them together.
有些图形是由两个或更多长方形组合而成的。我们可以把图形分成几个小长方形，分别求出每个小长方形的面积，再把它们加起来。
For example, an L-shaped figure can be divided into a large rectangle and a small rectangle. Add the two areas to find the total area.
例如，一个 L 形图形可以分成一个大长方形和一个小长方形。把两个面积相加，就得到总面积。
Always check the side lengths carefully on the diagram before multiplying.
在相乘之前，一定要仔细检查图中每条边的长度。
7. Perimeter vs. Area | 周长与面积的比较
Perimeter and area are different: perimeter measures the distance around a shape, while area measures the space inside a shape.
周长和面积是不同的概念：周长测量图形一周的距离，而面积测量图形内部的空间。
Two shapes can have the same perimeter but different areas, or the same area but different perimeters.
两个图形的周长可能相同但面积不同，也可能面积相同但周长不同。
| Measurement | What It Tells Us | Unit |
| Perimeter | Distance around the outside | cm, m, ft |
| Area | Space inside the shape | cm², m² |
The table above shows an important difference: perimeter uses ordinary length units, but area uses square units.
上面的表格展示了一个重要区别：周长使用普通的长度单位，而面积使用平方单位。
8. Same Perimeter, Different Area | 周长相同，面积不同
A rectangle with perimeter 16 cm could be 7 cm × 1 cm with area 7 cm², 6 cm × 2 cm with area 12 cm², 5 cm × 3 cm with area 15 cm², or 4 cm × 4 cm with area 16 cm².
周长为 16 厘米的长方形，可能是 7 厘米 × 1 厘米（面积 7 平方厘米），或 6 厘米 × 2 厘米（面积 12 平方厘米），或 5 厘米 × 3 厘米（面积 15 平方厘米），或 4 厘米 × 4 厘米（面积 16 平方厘米）。
For a fixed perimeter, a square gives the greatest area of all rectangles.
当周长固定时，在所有长方形中，正方形的面积最大。
This idea helps builders and designers use materials wisely to enclose as much space as possible.
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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