基本几何公式

在数学中，几何是一门研究学科，也是分析形状和结构及其特性的学科。下面给出的文章说明了用于计算特定形状的各种参数的标准固定或派生几何公式。这些公式用于确定未知的边、角度或其他数量。

基本几何公式

公式是推导两个或多个物理量之间的关系或数学关系而形成的数学规则。公式通常在数学符号的帮助下以符号形式表示。这些公式的符号表示由变量、常数、操作符号和项组成。

几何公式是用于计算形状参数的标准派生公式。这些参数是面积、体积、周长、周长、总表面积、侧表面积等。在几何学下研究的每种形状都有自己独特的公式。这些公式在下面列出。

正方形

• The perimeter of Square = 4a
• The area of Square = a²

Where ‘a’ is the length of the sides of a square

长方形

• Perimeter of Rectangle = 2(l + b)
• The area of Rectangle = l × b

Where ‘l’ is Length and ‘b’ is Breadth

三角形

• Area of Triangle = A = 1/2 × b × h

Where ‘b’ is the base of the triangle 

and ‘h’ is the height of the triangle

梯形

• Area of Trapezoid = A =1/2 × (b1 + b2) × h

Where b1 and b2 are the bases of the Trapezoid

and, h is the height of the Trapezoid

圆圈

• Area of Circle = A = π × r2
• Circumference of Circle = A = 2πr

Where ‘r’ is the radius of a Circle

立方体

• Surface Area of Cube = 6a²

Where ‘a’ is the length of the sides of the Cube

圆筒

• The curved surface area of Cylinder = 2πrh
• The total surface area of Cylinder = 2πr(r + h)
• The volume of Cylinder = V = πr2h

Where ‘r’ is the radius of the base of Cylinder

 and ‘h’ is the height of Cylinder

锥体

• The curved surface area of a cone = πrl
• Total surface area of cone = πr(r + l) = πr[r + √(h² + r²)]
• Volume of a Cone = V =1/2× πr²h

Here, ‘r’ is the radius of the base of Cone 

and h is  height of the Cone

领域

• Surface Area of a Sphere = 4πr²
• The volume of a Sphere = 4/3 × πr³

Where r is the radius of the Sphere

示例问题

问题1.如果一个圆的半径是14cm。找到给定圆的面积。

解决方案：

Given

The radius of the circle is 14cm.

We have,

Area of the circle (A)=πr²

=>22/7 x 14 x 14

=>616cm²

问题 2. 求底边为 12 厘米，高为 8 厘米的三角形的面积。

解决方案：

Given

The base of the triangle is 12cm.

The height of the triangle is 8cm.

We have,

Area of triangle(A)=1/2 x b x h

=>1/2 x 12 x 8

=>48cm²

问题 3. 求给定长 10 厘米宽 4 厘米的矩形的周长。

解决方案：

Given

The length of the rectangle is 10cm.

The breadth of the rectangle is 4cm.

We have,

Perimeter of rectangle(P)= 2(l+b)

=>2(10+4)

=>2 x 14

=>28cm

问题 4. 求一个长为 5 厘米的正方形的周长。

解决方案：

Given

The length of the square is 5cm.

We have,

The perimeter of the square(P)= 4l

=> 4 x 5

=>20cm

问题 5. 求一个半径为 9 厘米的球体的体积。

解决方案：

Given

The radius of the sphere is 9cm.

We have

The volume of a sphere(V)=4/3 πr³

=>4/3 x 22/7 x (9)³

=>3054.85cm³

问题 6. 计算底边为 8 厘米和 10 厘米，高为 12 厘米的梯形的面积。

解决方案：

Given

Let the bases of the trapezoid be b1 and b2 with values 8cm and 10cm respectively.

The height of the trapezoid is 12cm.

We have,

Area of Trapezoid = A =1/2 × (b1 + b2) × h

=>1/2 x (8 +10) x 12

=>1/2 x 18 x 12

=>216/2

=>108cm²

问题 7. 求给定圆锥的体积，半径为 6 厘米，高为 12 厘米。

解决方案：

Given

The radius of the cone is 6cm.

The height of the given cone is 12cm

We have,

Volume of a Cone = V =1/2× πr²h

=>1/2 x 22/7 x (6)² x 12

=>9504/14

=>678.85cm³

习题 8. 计算一个半径为 4cm、高为 8cm 的圆柱体的曲面面积。

解决方案：

Given

The radius of the cylinder is 4cm.

The height of the cylinder is 8cm.

We have,

Curved surface area= 2πrh

=>2 x 22/7 x 4 x 8

=>201.14cm²

问题 9. 计算边长为 3 厘米的立方体的面积。

解决方案：

Given

The length of a side is 3cm.

We have,

Area of cube(A)= 6a²

=> 6 x 3 x3

=>54cm²