📚 enVision Grade 3 Lesson 17-1: Understand Perimeter | 理解周长
Welcome to Lesson 17-1 from enVision Grade 3! In this lesson, we will explore the idea of perimeter: the distance all the way around a shape. You will learn how to measure it, how to add side lengths, and why perimeter matters in the real world.
欢迎来到 enVision 三年级第 17-1 课！在本课中，我们将探索“周长”的概念：绕一个图形一周的距离。你将学习如何测量周长、如何把各边长度相加，以及为什么周长在现实世界中很重要。
1. What Is Perimeter? | 什么是周长？
Perimeter is the total distance around the outside of a two-dimensional shape. Imagine walking around a playground fence: the distance you walk from the starting point all the way back to the same point is the perimeter.
周长是一个二维图形外边缘的总距离。想象你沿着操场围栏走一圈：从起点出发，绕一整圈回到同一个起点所走的距离就是周长。
To find perimeter, you simply add the lengths of all the sides. If a side is curved, we would need special tools, but in this lesson we only work with straight-sided shapes like triangles, rectangles, and squares.
要求周长，只需要把所有边的长度加起来。如果一条边是弯曲的，我们就需要特殊工具，但在本课中我们只研究三角形、长方形和正方形等直边图形。
Perimeter is measured in units of length, such as centimeters (cm), meters (m), inches (in), and feet (ft).
周长的单位是长度单位，比如厘米（cm）、米（m）、英寸（in）和英尺（ft）。
The word "perimeter" comes from Greek words meaning "around" and "measure."
“perimeter”一词来自希腊语，意思是“围绕”和“测量”。
2. Finding Perimeter by Adding Side Lengths | 用“边长相加”求周长
example, a triangle with sides 3 cm, 4 cm, and 5 cm has a perimeter of 3 + 4 + 5 = 12 cm.
求任何多边形周长最基本的方法，就是把所有边的长度都加起来。例如，一个三角形的三边分别是 3 cm、4 cm 和 5 cm，那么它的周长就是 3 + 4 + 5 = 12 cm。
Let' wo long sides of 8 cm and two short sides of 3 cm. Its perimeter is 8 + 3 + 8 + 3 = 22 cm.
再看一个例子。一个长方形有两条长边是 8 cm，两条短边是 3 cm。它的周长是 8 + 3 + 8 + 3 = 22 cm。
Perimeter = Side 1 + Side 2 + Side 3 + ...
周长 = 边 1 + 边 2 + 边 3 + ...
3. Perimeter of a Rectangle | 长方形的周长
A rectangle has two pairs of equal sides. We call the longer side the length (l) and the shorter side the width (w).
长方形有两组相等的对边。我们把较长的边叫作长（l），较短的边叫作宽（w）。
Because the opposite sides are equal, we can use two useful formulas:
因为对边相等，所以我们可以使用两个有用的公式：
Perimeter = length + width + length + width
周长 = 长 + 宽 + 长 + 宽
Perimeter = 2 × (length + width)
周长 = 2 × （长 + 宽）
ngle has length 10 cm and width 4 cm, then its perimeter is 2 × (10 + 4) = 2 × 14 = 28 cm.
例如，一个长方形的长是 10 cm，宽是 4 cm，那么它的周长是 2 ×（10 + 4）= 2 × 14 = 28 cm。
| Shape 图形 | Formula 公式 |
| Rectangle 长方形 | P = 2 × (l + w) |
| Square 正方形 | P = 4 × s |
| Triangle 三角形 | P = a + b + c |
4. Perimeter of a Square | 正方形的周长
A square has four equal sides. If one side is called s, then all four sides are exactly the same length.
正方形有四条相等的边。如果一条边记作 s，那么四条边都完全相同。
So the perimeter of a square is easy to calculate:
所以正方形的周长很容易计算：
Perimeter = s + s + s + s = 4 × s
周长 = s + s + s + s = 4 × s
hat a 7 cm by 7 cm square and a 10 cm by 4 cm rectangle can have the same perimeter, even though their shapes are different!
例如：一个正方形的边长是 7 cm。它的周长是 4 × 7 = 28 cm。注意，一个边长为 7 cm 的正方形和一个长 10 cm、宽 4 cm 的长方形可以有相同的周长，即使它们的形状完全不同！
5. Finding a Missing Side Length | 求未知边长
Sometimes you know the perimeter of a shape and the lengths of most sides, but one side is missing. You can find it by subtracting the known sides from the total perimeter.
有时候，你知道一个图形的周长和大多数边的长度，但有一条边的长度不知道。你可以从总周长中减去已知的各边来求出它。
a perimeter of 20 cm. Two sides are 6 cm and 8 cm. The missing side is 20 − 6 − 8 = 6 cm.
例如：一个三角形的周长是 20 cm。其中两条边分别是 6 cm 和 8 cm。未知的那条边是 20 − 6 − 8 = 6 cm。
one side, you can find the other side using the formula: length = (perimeter ÷ 2) − width.
对于长方形，如果你知道周长和一条边，可以用这个公式求另一边：长 = （周长 ÷ 2）− 宽。
Missing side = Perimeter − Sum of known sides
未知边 = 周长 − 已知各边之和
6. Perimeter in the Real World | 周长在现实生活中的应用
Perimeter is not just a math exercise; we use it every day. Builders use perimeter to order fencing, crown molding, or baseboards. Farmers use perimeter to plan fences around fields.
周长不只是数学练习，我们每天都会用到它。建筑工人用周长来订购围栏、装饰线条或踢脚线。农民用周长来规划农田周围的围栏。
To put a ribbon around a rectangular gift box, you need to know its perimeter (plus a little extra for the bow).
要用丝带绕长方形礼盒一圈，你需要知道它的周长（还要额外留一点打蝴蝶结）。
To build a fence around a soccer field, the groundskeeper must calculate the perimeter of the field.
要在足球场周围建围栏，场地管理员必须计算球场的周长。
When framing a picture, the perimeter tells you how much wood or metal you need.
给一幅画装框时，周长告诉你要用多少木头或金属材料。
7. Perimeter vs. Area | 周长与面积的区别
Perimeter and area are easy to confuse, but they measure very different things.
周长和面积很容易混淆，但它们测量的内容完全不同。
| Perimeter 周长 | Area 面积 |
| Distance around a shape 图形一圈的距离 | Space inside a shape 图形内部的空间 |
| Measured in units (cm, m, ft) 用单位表示（cm, m, ft） | Measured in square units (cm², m²) 用平方单位表示（cm², m²） |
| Found by adding side lengths 通过加各边长度得到 | Found by multiplying length × width 通过长 × 宽得到 |
Think of perimeter as the fence around a yard and area as the grass inside the yard.
把周长想象成院子周围的栅栏，而面积是院子里的草坪。
8. Practice Problems | 练习题目
Try these problems on your own. Answers are shown below.
请独立完成这些题目。答案在下方。
A rectangle has length 12 cm and width 5 cm. Find its perimeter.
一个长方形长 12 cm，宽 5 cm。求它的周长。
A square has side length 9 m. Find its perimeter.
一个正方形边长 9 m。求它的周长。
A triangle has sides 7 cm, 8 cm, and 9 cm. What is its perimeter?
一个三角形的三边是 7 cm、8 cm 和 9 cm。它的周长是多少？
The perimeter of a rectangle is 30 cm. Its length is 9 cm. Find its width.
一个长方形的周长是 30 cm。长是 9 cm。求它的宽。
Answers: 34 cm, 36 m, 24 cm, 6 cm
答案：34 cm，36 m，24 cm，6 cm
9. Tips and Tricks | 小技巧与提示
Here are some friendly tips to help you master perimeter.
这里有一些帮助你掌握周长的小技巧。
Always write down the unit (cm, m, in, ft) with your answer. Perimeter is a length, not just a number.
写答案时一定要带上单位（cm、m、in、ft）。周长是一个长度，而不只是一个数字。
If a shape has equal sides, use multiplication instead of repeated addition to save time.
如果图形有相等的边，用乘法代替重复加法可以节省时间。
Draw the shape and label every side before adding. This helps you avoid missing a side.
先画出图形并标注每条边，再加起来。这能帮助你避免漏掉某一条边。
Double-check that all side lengths are in the same unit before adding.
相加前，先检查所有边长是否使用同一个单位。
10. Summary | 本课总结
In this lesson, you learned that perimeter is the distance around a shape. You practiced adding side lengths, using formulas for rectangles and squares, finding missing sides, and applying perimeter to real-world situations.
在本课中，你学习了周长是绕图形一周的距离。你练习了边长相加、使用长方形和正方形的周长公式、求未知边长，以及把周长应用到现实情境中。
+ w). For a square, use P = 4 × s. Keep practicing, and perimeter will become your friend!
记住：对于任何多边形，只要把所有边加起来即可。对于长方形，用 P = 2 ×（l + w）。对于正方形，用 P = 4 × s。不断练习，周长就会成为你的好朋友！
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图