怎么计算正方形的周长

平面图形的周长就是它外围一圈的长度，即边长的总和^[1] 。根据定义，正方形是四条边都相等，并且四个角都是直角的四边形^[2] 。由于四条边长度都相等，所以计算正方形的周长是一件很简单的事。本文首先会介绍已知正方形的边长求周长的方法，然后会介绍已知正方形的面积求周长的方法，最后会介绍在已知圆半径的情况下，计算圆内接正方形周长的方法。

步骤

已知一条边长，计算正方形周长

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/4f\/Calculate-the-Perimeter-of-a-Square-Step-1-Version-3.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-1-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/4f\/Calculate-the-Perimeter-of-a-Square-Step-1-Version-3.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 回忆求正方形周长的公式。如果正方形的边长用S表示，那么周长就是四倍的边长，即P=4s。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/ae\/Calculate-the-Perimeter-of-a-Square-Step-2-Version-4.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-2-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/ae\/Calculate-the-Perimeter-of-a-Square-Step-2-Version-4.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-2-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 求正方形的边长，然后再乘以4。根据具体的问题，你可能需要用尺子量出边长，或者参考页面中的信息，得到正方形的边长。下面是几个例子：
   • 若正方形的一条边长为4，则P=4*4，即16。
   • 若正方形的一条边长为6，则P=4*6，即24。

仅知道正方形面积时，计算其周长

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/fc\/Calculate-the-Perimeter-of-a-Square-Step-3-Version-3.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-3-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/fc\/Calculate-the-Perimeter-of-a-Square-Step-3-Version-3.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-3-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 了解正方形的面积公式。矩形（正方形是特殊的矩形）的面积等于长乘以宽^[3] 。由于正方形的长和宽相等，那么边长为s的正方形的面积就是s*s，即A = s²。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/bc\/Calculate-the-Perimeter-of-a-Square-Step-4-Version-3.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-4-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/bc\/Calculate-the-Perimeter-of-a-Square-Step-4-Version-3.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-4-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 求面积的平方根。面积的平方根就是正方形的边长。对于大部分数字，你需要用计算器才能求出它的平方根。先在计算器上输入数字，然后按下平方根键(√)，就可以得到该数字的平方根。你还可以学习手算平方根的方法。
   • 如果面积是20，那么边长s =√20，即4.472
   • 如果面积是25，那么边长s =√25，即5
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/c\/c4\/Calculate-the-Perimeter-of-a-Square-Step-5-Version-2.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-5-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/c\/c4\/Calculate-the-Perimeter-of-a-Square-Step-5-Version-2.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 用边长乘以4。用你刚计算出来的边长s，代入周长计算公式P = 4s。最终结果就是正方形的周长。
   • 对于面积为20，边长4.472的正方形，周长为P = 4 * 4.472，即17.888
   • 对于面积为25，边长5的正方形，周长为P = 4 * 5，即20

计算圆内接正方形的周长

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/72\/Calculate-the-Perimeter-of-a-Square-Step-6-Version-2.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-6-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/72\/Calculate-the-Perimeter-of-a-Square-Step-6-Version-2.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-6-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 了解什么是圆内接正方形。在GMAT和GRE考试中，这个概念经常会出现，所以很有必要了解这个概念。圆内接正方形就是画在圆里的正方形，正方形的四个顶点都在圆周上。^[4]
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/a7\/Calculate-the-Perimeter-of-a-Square-Step-7-Version-2.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-7-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/a7\/Calculate-the-Perimeter-of-a-Square-Step-7-Version-2.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 了解圆半径和正方形边长的关系。圆心到正方形任意一角的距离就是圆的半径。为了求出边长s，我们需要先想象将正方形沿对角线切成两个直角三角形，每个三角形都有相同长度的直角边长a和b以及斜边c，其中斜边长等于圆半径的两倍，即2r。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/47\/Calculate-the-Perimeter-of-a-Square-Step-8-Version-2.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-8-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/47\/Calculate-the-Perimeter-of-a-Square-Step-8-Version-2.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-8-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 使用勾股定理求正方形的边长。勾股定理描述了直角三角形的两条直角边a和b与斜边c之间的关系，即a² + b² = c²。^[5] 因为a和b相等（我们计算的是正方形），而且c = 2r，所以我们就可以列出方程求解：
   • a² + a² = (2r)²，进行化简：
   • 2a² = 4(r)²，两边同时除以2：
   • (a²) = 2(r)²，对两边开方：
   • a = √(2r)。边长s就是√(2r)。
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/91\/Calculate-the-Perimeter-of-a-Square-Step-9-Version-2.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-9-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/91\/Calculate-the-Perimeter-of-a-Square-Step-9-Version-2.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-9-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 用边长乘以4。在本例中，正方形的周长P = 4√(2r)。根据分配律，4√(2r)等于4√2 * √r，所以我们可以直接代入下面的方程：P = 5.657r，其中r是外接圆的半径。^[6]
5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/17\/Calculate-the-Perimeter-of-a-Square-Step-10-Version-3.jpg\/v4-460px-Calculate-the-Perimeter-of-a-Square-Step-10-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/17\/Calculate-the-Perimeter-of-a-Square-Step-10-Version-3.jpg\/v4-728px-Calculate-the-Perimeter-of-a-Square-Step-10-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 求解例题。已知圆的半径为10，那么直径就是20。使用勾股定理可得2(a²) = 20²，即2a² = 400。两边同时除以2，得a² = 200。同时求两边的平方根，得a = 14.142。同时乘以4，就可以得到正方形的周长，即P = 56.57。
   • 注意，10乘以5.657，即10 * 5.567 = 56.57，这个过程比较简单，很容易算。但是考试中给出的数字可能并不好算，所以最好牢记计算过程。