📏 周长与面积：围一圈 vs 铺一层📏 Perimeter & Area: Around vs Inside
上一片里，小算盘机器人比过“形状一样、大小成比例”。这一片它回到自家菜园，量清楚两件最容易混的事：篱笆「围一圈」有多长，菜地「铺一层」有多大。Last leaf, the little abacus robot compared shapes that match and scale. Now it is back in its own garden, sorting out two easily-mixed ideas: how long the fence is “around”, and how big the plot is “inside”.
第 1 步：围一圈 vs 铺一层Step 1: Around vs inside
先看这块菜地——它同时藏着两个量。Look at the vegetable plot — it hides two different measures at once.
机器人用篱笆把菜地围起来：篱笆总长 20 米，这是周长（perimeter）——沿着边边走一圈的长度；篱笆里面能种多少，看的是面积（area）——铺满整个面的大小。一个管“边”，一个管“面”。The robot fences its plot: the fence totals 20 m — that's the perimeter, one lap along the edge. How much can grow inside depends on the area — the size of the whole surface. One measures the edge, the other the surface.
那它俩到底怎么算？机器人把一块地画成了地图。So how do you compute each one? The robot drew a plot as a map to show it.
第 2 步：描边算周长，涂色算面积Step 2: Trace the edge vs colour the surface
只描边：算的是周长，单位是米；整块涂色：算的是面积，单位是平方米（m²）。长方形：周长 =（长 + 宽）× 2；面积 = 长 × 宽。这块 5 米 × 4 米的地：周长 18 米，面积 20 平方米——数字相近，意义完全不同。Tracing only the outline gives the perimeter, measured in metres. Colouring the whole thing in gives the area, measured in square metres (m²). For a rectangle: perimeter = (length + width) × 2; area = length × width. This 5 m × 4 m plot: perimeter 18 m, area 20 m² — similar numbers, completely different meanings.
为什么要分成“米”和“平方米”两种单位？到施工现场看看。Why two different units — metres and square metres? Let's visit a building site.
第 3 步：铺满一间屋Step 3: Tiling a whole room
给房间铺地砖，算的是面积：地面 6 米 × 4 米 = 24 平方米，每块砖 1 平方米，正好 24 块。而沿墙脚围一圈踢脚线，算的是周长。买材料前先想清楚：我量的是“边”，还是“面”？Tiling a floor is area work: 6 m × 4 m = 24 m², and with 1 m² tiles that's exactly 24 tiles. Running skirting along the wall edges is perimeter work. Before buying materials, ask: am I measuring the edge, or the surface?
🎮 你来围菜地（30 秒）🎮 Your turn: fence a plot (30 seconds)
道理讲完了。篱笆总长固定 20 米——拖拖滑块，把菜地面积围到最大试试。Theory done. The fence is a fixed 20 m — drag the slider and try to make the plot's area as big as possible.
一句话记住它：周长是围一圈的边框长度（米），面积是铺一层的大小（平方米）；周长一样，面积可以不同——正方形最大。Remember it in one line: perimeter is the length of the edge (metres); area is the size of the surface (square metres). Same perimeter, different areas — the square is the biggest.
周长：沿边边走一圈，单位是米（m）Perimeter: one lap along the edge, measured in metres (m)面积：铺满整个面，单位是平方米（m²）Area: the whole surface, measured in square metres (m²)周长固定 20 米时，长 5 米 × 宽 5 米的正方形面积最大（25 平方米）With a fixed 20 m fence, the 5 m × 5 m square holds the most (25 m²)
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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