Perimeter of Common Shapes | 常见图形的周长

📚 Perimeter of Common Shapes | 常见图形的周长

Perimeter is the total distance around the outside of a two-dimensional shape. When you walk around the edge of a playground, the distance you walk is its perimeter. In this lesson, we will learn how to find the perimeter of common shapes such as rectangles, squares, triangles, and other polygons.

周长是二维图形外边界一周的总长度。当你沿着操场的边缘走一圈，你所走的距离就是它的周长。本节课我们将学习如何求长方形、正方形、三角形以及其他多边形等常见图形的周长。

1. What Is Perimeter? | 什么是周长？

Perimeter means “measure around.” Every polygon has sides, and the perimeter is the sum of the lengths of all its sides. Think of perimeter as the length of fence needed to enclose a shape.

周长意为”围量一周”。每个多边形都有边，周长就是所有边长度的总和。可以把周长想象成围住一个图形所需的围栏长度。

For example, a triangle with sides 3 cm, 4 cm, and 5 cm has a perimeter of 3 + 4 + 5 = 12 cm. We always write the unit of length, such as cm, m, or mm.

例如，一个边长分别为3厘米、4厘米和5厘米的三角形，其周长为3 + 4 + 5 = 12厘米。我们总是要写上长度单位，如厘米、米或毫米。

2. Units of Perimeter | 周长的单位

Perimeter is a length, so it uses one-dimensional units: millimetres (mm), centimetres (cm), metres (m), and kilometres (km). The unit must match the sides.

周长是一种长度，因此使用一维单位：毫米（mm）、厘米（cm）、米（m）和千米（km）。单位必须与各边一致。

Use mm for very small objects, such as a paperclip.
中文配英文：毫米用于很小的物体，如回形针。
Use cm for objects like a book or a phone.
中文配英文：厘米用于书本或手机等物体。
Use m for rooms, gardens, or fields.
中文配英文：米用于房间、花园或田野。

If all side lengths are in the same unit, the perimeter is in that unit. If they are different, convert them first.

如果所有边长使用相同单位，那么周长也使用该单位。如果单位不同，需要先进行换算。

3. Perimeter of a Rectangle | 长方形的周长

A rectangle has two pairs of equal sides: two lengths and two widths. The perimeter is the sum of all four sides, or twice the length plus twice the width.

长方形有两组相等的边：两条长和两条宽。周长就是四条边的总和，也就是两倍长加两倍宽。

Perimeter of rectangle = 2 × (length + width)

For example, a rectangle with length 8 cm and width 3 cm has perimeter 2 × (8 + 3) = 2 × 11 = 22 cm.

例如，一个长为8厘米、宽为3厘米的长方形，其周长为2 × (8 + 3) = 2 × 11 = 22厘米。

Remember that length is usually the longer side and width is the shorter side.

记住，通常较长的一边是长，较短的一边是宽。

4. Perimeter of a Square | 正方形的周长

A square has four equal sides, so its perimeter is simply four times the length of one side.

正方形有四条相等的边，所以它的周长就是一条边长的四倍。

Perimeter of square = 4 × side length

If a square has a side length of 6 cm, its perimeter is 4 × 6 = 24 cm. This shortcut is much faster than adding 6 + 6 + 6 + 6.

如果一个正方形的边长是6厘米，那么它的周长是4 × 6 = 24厘米。这个简便方法比6 + 6 + 6 + 6快得多。

A square is a special rectangle, so the rectangle formula also works: 2 × (6 + 6) = 24 cm.

正方形是一种特殊的长方形，所以长方形公式也同样适用：2 × (6 + 6) = 24厘米。

5. Perimeter of a Triangle | 三角形的周长

A triangle has three sides. To find its perimeter, add the lengths of all three sides. There is no shortcut formula unless the triangle has special properties.

三角形有三条边。要求周长，只需把三条边的长度相加。除非三角形有特殊性质，否则没有简便公式。

Perimeter of triangle = side a + side b + side c

For an equilateral triangle, all sides are equal, so the perimeter is 3 × side length. For other triangles, just add directly.

对于等边三角形，三条边都相等，所以周长是3 × 边长。对于其他三角形，直接相加即可。

Example: a triangle with sides 7 cm, 5 cm, and 9 cm has perimeter 7 + 5 + 9 = 21 cm.

例如：一个边长分别为7厘米、5厘米和9厘米的三角形，其周长为7 + 5 + 9 = 21厘米。

6. Perimeter of Other Polygons | 其他多边形的周长

Any polygon can be measured by adding all of its side lengths. A pentagon has five sides, a hexagon has six sides, and an octagon has eight sides.

任何多边形都可以通过将所有边长相加来测量。五边形有五条边，六边形有六条边，八边形有八条边。

For a regular polygon, all sides are equal, so the perimeter is the number of sides multiplied by the side length.

对于正多边形，所有边都相等，所以周长等于边数乘以边长。

Perimeter of regular polygon = number of sides × side length

For irregular polygons, simply add every side individually. Always label the diagram with each side length before adding.

对于不规则多边形，只需逐边相加。在相加之前，先在图上标出每条边的长度。

7. Using Addition and Multiplication | 用加法和乘法

Addition and multiplication are both useful for perimeter. Addition works for every shape, while multiplication is a shortcut for shapes with equal sides.

加法和乘法对求周长都很有用。加法适用于所有图形，而乘法是处理等边图形的简便方法。

Shape	Fast Method
Square (side s)	4 × s
Rectangle (l and w)	2 × (l + w)
Regular pentagon (side s)	5 × s

Use multiplication only when you are sure the sides are equal. Otherwise, use addition to avoid mistakes.

只有确定各边相等时才使用乘法。否则，应使用加法以避免错误。

8. Finding a Missing Side | 求未知边长

Sometimes you know the perimeter and all but one side. To find the missing side, subtract the known side lengths from the total perimeter.

有时你知道周长以及除了某一边之外的所有边长。要求未知边，只需从总周长中减去已知各边的长度。

Example: a rectangle has perimeter 30 cm and width 6 cm. Since opposite sides are equal, perimeter = 2 × length + 2 × 6. So 30 = 2 × length + 12, and 2 × length = 18, so length = 9 cm.

例如：一个长方形周长为30厘米，宽为6厘米。因为对边相等，周长 = 2 × 长 + 2 × 6。所以30 = 2 × 长 + 12，2 × 长 = 18，因此长为9厘米。

For an irregular polygon, subtract the known side lengths one by one from the perimeter to find the remaining side.

对于不规则多边形，从周长中依次减去已知边长，即可求出剩余边的长度。

9. Real-World Applications | 实际应用

Perimeter is used in many everyday situations. Farmers use it to build fences, builders use it to install baseboards, and designers use it to place borders around pictures.

周长在许多日常场景中都会用到。农民用它修建围栏，建筑工人用它安装踢脚线，设计师用它为图片加边框。

Fencing a garden: find the perimeter of the garden to know how much fence to buy.
中文配对：围花园：求出花园的周长，就知道需要买多少围栏。
Framing a photo: the frame length equals the perimeter of the photo.
中文配对：装照片框：相框的长度等于照片的周长。
Running track: one lap around an athletic track is its perimeter.
中文配对：跑道：绕运动场跑一圈就是它的周长。

Understanding perimeter helps you solve practical measurement problems accurately.

理解周长有助于你准确解决实际的测量问题。

10. Common Mistakes to Avoid | 常见错误

Several common mistakes appear when students find perimeter. Avoid them to improve accuracy.

学生在求周长时会出现几个常见错误。避免这些错误可以提高准确率。

Adding only two sides instead of all sides.
中文配对：只加两条边，而不是所有边。
Forgetting the unit, such as cm or m.
中文配对：忘记写单位，如厘米或米。
Confusing perimeter with area. Perimeter is length around; area is space inside.
中文配对：混淆周长与面积。周长是外围长度，面积是内部空间。

Always check if the shape is a rectangle or square and use the correct formula. For any shape, adding all sides never fails.

始终检查图形是否为长方形或正方形，并选择正确的公式。对于任何图形，将所有边相加一定不会错。

11. Practice Questions | 练习

Now try these questions to check your understanding.

现在尝试以下问题来检验你的理解。

Find the perimeter of a rectangle with length 12 cm and width 7 cm.
中文配对：求一个长方形的周长，长为12厘米，宽为7厘米。
Find the perimeter of a square with side length 9 m.
中文配对：求一个正方形的周长，边长为9米。
A triangle has sides 6 cm, 8 cm, and 10 cm. Find its perimeter.
中文配对：一个三角形的三边长为6厘米、8厘米和10厘米，求它的周长。

Answers: 1) 2 × (12 + 7) = 38 cm. 2) 4 × 9 = 36 m. 3) 6 + 8 + 10 = 24 cm.

答案：1) 2 × (12 + 7) = 38厘米。2) 4 × 9 = 36米。3) 6 + 8 + 10 = 24厘米。

12. Key Takeaways | 关键要点

The most important idea is that perimeter is the total distance around a shape. You can always find it by adding all side lengths.

最重要的概念是：周长是图形外围的总距离。你总可以通过将各边相加来求得它。

Perimeter is measured in length units: mm, cm, m, km.
中文配对：周长用长度单位表示：毫米、厘米、米、千米。
Rectangle formula: P = 2 × (length + width).
中文配对：长方形公式：P = 2 × (长 + 宽)。
Square formula: P = 4 × side.
中文配对：正方形公式：P = 4 × 边长。
For any polygon, add every side length.
中文配对：对于任何多边形，将每条边相加。

Practice these methods and you will solve perimeter problems quickly and correctly.

勤加练习这些方法，你就能迅速而正确地解决周长问题。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Perimeter of Common Shapes | 常见图形的周长