三角形和圆形可以有相同的周长吗？

测量是数学的一部分，涉及几何图形的研究及其参数（如面积、长度、体积、周长、表面积等）的计算。该研究涉及二维和三维形状，其中二维形状涉及形状的长度和宽度。它不处理形状的厚度。而且，3D 形状具有长度、宽度和高度的尺寸。

测量公式的公式图表

在标准导出公式的帮助下确定测量不同形状的参数。这些公式使计算更便于推导解决方案。

2D shapes	Formulas
Triangle	1/2 base × height
Rectangle	perimeter = 2(length + breadth) Area = length × breadth
Square	Area = (side)2 Perimeter = 4(side)
Circle	Diameter = 2 × radius Area = πr2

3D shapes	Formulas
Sphere	Volume = 4/3πr3 Total surface area = πr(l + radius)
Cube	Volume = (side)3 Lateral surface area = 4(side)2  Total surface area = 6(side)2
Cuboid	Volume = length × width × height Lateral surface area = 2h(l + b) Total surface area = 2(lb + lh + bh)
Cone	Volume = 1/3 πr2h Total surface area = πr(l + radius)

三角形和圆形可以有相同的周长吗？

回答：

An equilateral triangle and a circle do not have the same perimeter. Let P_t  be the perimeter of an equilateral triangle, and, P_c is the perimeter of a circle. Now, evaluate the perimeter of an equilateral triangle and a circle.

The perimeter of an equilateral triangle by standard mensuration formula,

P_t  = a + b + c 

As the given triangle is equilateral it’s all sides are equal.

P_t = x + x + x

P_t = 3x

x = P_t/3

Circumference or perimeter of the circle,

P_c = 2πr

x = P_c/2π

The perimeter of the triangle is greater than a circle.

The perimeter of the triangle > Perimeter of the circle

P_t > P_c

Hence, the perimeter of an equilateral triangle and a square are the same.

示例问题

问题1：如果一个圆的半径为14cm。找到它的区域。

解决方案：

Given,

Radius of circle(r) =14cm

Area(A) = ?

Now,

Area = πr²

A = 22/7 × 14 × 14

A = 22 × 2 × 14

A = 616cm²

Hence, the area of given circle is 616 cm².

问题 2：菱形的对角线长度分别为 5cm 和 8cm。计算它的面积。

解决方案：

Given,

Diagonal 1(d₁) = 5cm

Diagonal 2(d₂) = 8cm

Now,

Area of rhombus(A) = 1/2 × d₁ × d₂

A = 1/2 × 5 × 8

A = 40cm²

Hence, the area of rhombus is 40cm².

问题3：如果正方形的一边是20cm。它的周长和面积是多少？

解决方案：

Given,

Side of square = 20cm

Now,

Perimeter of square(P) = 4(side)

P = 4 × 20

P = 80cm

Then, 

Area of square(A) = (side)²

A = 20 × 20 

A = 400cm²

Hence, the perimeter of a square is 80cm and its area is 400cm².

问题：求一个长10cm、宽4cm、高5cm的长方体的体积。

解决方案：

Length(l) = 10cm

Breadth(b) = 4cm

Height (h) = 5cm

Now,

Volume of cuboid (V) = length × breadth × height

V = 10 × 4 × 5

V = 200cm³

Hence, the volume of cuboid is 200cm³.