平方公式

正方形是具有四个相等边的四边形。我们周围有许多呈方形的物品。每个正方形的区别在于其相等的边和等于 90° 的内角。正方形是具有四个边的封闭二维 (2D) 形式。它有四个相等且平行的边。正方形是相邻边等长的矩形。这表明它是一个边长相等的四边形。正方形中的每个角都是直角。

Square的一些属性

• 正方形有四个等长的边。
• 正方形的对角线相等。
• 正方形的对角线相交成直角。
• 正方形的四个角都是直角。

广场面积

正方形面积的计算公式：正方形面积（A）

= 长度 = 宽度

= AB = BD = 一个

= 一 × 一

Area of square = a² where, a is the side of the square.

正方形的周长

多边形所有边的总和称为周长。它将是正方形四个相等边的总和，或正方形边长的四倍。

正方形的周长=正方形所有边的总和

= a + a + a + a

Perimeter of square = 4a units

因此，4a 是正方形的周长，每边的长度等于“a”个单位。

正方形对角线公式

If diagonal is given then the area of the square is equal to d²/2.

示例问题

问题 1：正方形有一条边长为 24 厘米。计算它的面积，周长？

解决方案：

Given, Side of the square = 24 cm

Area of the square: = a² where, a is the side of the square.

Therefore , Area of the square = a × a 

= 24 × 24 

= 576 sq cm 

Perimeter of the square =  Sum of all sides of square

= a + a + a + a

= 4a 

= 4 × 24 

= 96 cm

 Hence the area of square is 576 sq. cm and the perimeter of square is 96 cm.

问题 2：求周长为 56 厘米的正方形的边长。

解决方案：

Given perimeter of the square = 56 cm

Lets suppose length of each side of the square = ‘a’ cm

Therefore, perimeter = 4a cm

56 = 4a 

Or a = 56/4

a = 14 cm

Thus, length of each side of square is 14 cm.

问题3：求边长为5m的正方形的面积？

解决方案：

Given, side (a) = 5 m

Area of the square = a × a

= 5 × 5

= 25 sq m 

问题 4： 给定正方形的周长为 16 厘米，求正方形相邻边的总和。

解决方案：

Given the perimeter of the square = 16 cm

Considering length of each side = ‘a’ cm, the perimeter = 4a cm

Perimeter of Square = Sum of all sides of square

= a + a + a + a

= 4a units

So, 16 = 4a

Or a = 16/4

= 4 cm

Since all sides of a square are of same length, then for the sum of adjacent sides, we can write the sum,

= a + a 

= 2a

Therefore, the sum of adjacent sides of the square = 2 × 4 = 8 cm.

问题 5：求一个周长为 420 英尺的方形公园的面积？

解决方案：

Given: Perimeter of the square park = 420 ft

As we know that, Perimeter of a square = 4 × side

4 × side = 420

Side = 420/4

Side = 105 ft

Formulae for the Area of a square = side²

Hence, Area of the square park = 105² 

= 105 × 105

= 11025 ft²

Thus, the area of a square park whose perimeter is 420 ft is 11025 ft².

问题 6：矩形地板长 40 m，宽 30 m。每块边长为 4 m 的方形瓷砖将用于覆盖地板。覆盖地板所需的瓷砖总数是多少？

解决方案：

Given, Length of the floor = 40 m, Breadth = 30 m

Area of the rectangular floor = length × breadth = 40 m × 30 m = 1200 sq. m

Side length of one tile = 4 m

Area of one tile = side × side

= 4 m × 4 m

= 16 sq. m

Now number of tiles needed = Total area of floor / area of one tile 

= 1200 /16

= 75 tiles 

Total 75 tiles are needed to cover the area of rectangular floor of 1200 sq m.

问题 7：求对角线为 15 m 的方形公园的面积？

解决方案：

Given: Diagonal of the square park = 15 m

Area of a square formula when diagonal is given = d²/2 

Hence, Area of the square park = 15²/ 2

= (15 × 15)/2

= 225/2

= 112.5 sq. m

Thus, the area of a square park whose diagonal is 15 m is 112.5 sq. m.