正方形和长方形可以有相同的面积和周长吗？

测量是数学的一个分支，它处理几何形状的重量、体积、面积、周长等参数的计算。测量涉及 2D 和 3D 形状。

在 2D 形状中，对象具有两个维度并放置在平面上。二维将只是对象的长度和宽度。它不处理物体的厚度。

对象的 3D 形状具有三个维度，并且存在于现实世界中。三个维度是高度、宽度和深度。

二维形状的公式

下面给出一些二维形状参数计算的标准公式：

• 长方形

Perimeter = 2(length + breadth)

Area = length × breadth

• 正方形

Area = (side)²

Perimeter = 4(side)

• 圆圈

Diameter = 2 × radius

Area = πr²

• 三角形

Area = 1/2 base × height

3D 形状的公式

下面给出一些三维形状参数计算的标准公式：

• 立方体

Volume = (side)³

Lateral surface area = 4(side)²

Total surface area = 6(side)²

• 长方体

Volume = length × width × height

Lateral surface area = 2h(l+b)

Total surface area = 2(lb+lh+bh)

• 领域

volume = 4/3πr³

Surface area = 4πr²

• 锥体

Volume = 1/3πr²h

Total surface area = πr(l+radius)

正方形和长方形可以有相同的面积和周长吗？

Evaluating area of square and rectangle.

According to the question we have to find out whether the area of two geometrical shapes square and rectangle are equal or not.

Let’s assume a square with its side length be l. And, a rectangle with length (l) and breadth (b).

Now,

Area of square = Area of rectangle

Using the standard formulas,

=>(side)² = length × breadth

=>l² = l × b

=>l = b

If b = 4, then, l = 4

Calculating the area of square and rectangle

Area of square = (side)²

                        = (l)² = l × l = 4 × 4 = 16

Area of rectangle = l × b

                           = 4 × 4 =16

Hence, the area of the square and rectangle can be the same.

Following the same method let’s evaluate the perimeter of a square and a rectangle.

Evaluating the perimeter of a square and rectangle

Let’s assume a square with its side length be l. And, a rectangle with length (l) and breadth (b).

Now,

Perimeter of square= perimeter of rectangle

=>4(side) = 2(length+breadth)

=>4l = 2(l+b)

=>4l = 2l+2b

=>4l-2l = 2b

=>2l = 2b

=>l = b

If l = 4 then, b = 4

Calculating perimeter of square = 4(side) 

                                                   = 4l = 4 × 4 = 16

Calculating perimeter of rectangle = 2(l+b)

                                                       = 2(4+4) = 2 × 8 = 16

Hence, a square and rectangle can have the same area and perimeter in certain conditions.

示例问题

问题 1.求底边为 9 厘米，高为 5 厘米的三角形的面积。

解决方案：

Given,

Base of triangle(b) = 9cm

Height of triangle(h) = 5cm

Now,

Area = 1/2 b × h

=>1/2 × (9 × 5)

=>45/2cm²

问题2. 一个长方形的面积是48cm ² 。如果它的长度为 8 厘米，请找到它的宽度。

鉴于，

Length (l) = 8cm

Area(A) = 48cm²

Now,

Area = l × b

=>48 = 8 × b

=>b = 48/8

=>b = 6cm

问题 3. 求一个边长为 15cm 的正方形的面积。

解决方案：

Given,

Side(l) = 15cm

Now,

Area = (side)²

          = l² = 15 × 15 = 225cm²

问题 4. 如果一个长方形长 10 厘米，宽 5 厘米。它的周长是多少？

解决方案：

Given,

Length(l) =10cm

Breadth(b) = 5cm

Now,

Perimeter = 2(l+b)

=>P = 2(10+5)

=>P = 2 × 15

=>P = 30cm