Formula for calculating the volume of a vertical prism, prism shape

A prism is a polygon with two parallel and equal bases and parallelogram side faces.

Comment:

• The lateral faces of a prism are equal and parallel to each other.
• The lateral faces are parallelograms.
• The two bases of a prism are two equal polygons.

What is the formula for calculating the volume of a prism (V prism), the formula for calculating the volume of a vertical prism? Please refer to the article below.

Table of Contents

• 1. Volume of a vertical prism
• 3. Classification of prisms
  • Regular prism
  • Right prism
• 4. Example of calculating the volume of a vertical prism 

1. Volume of a vertical prism

Formula for calculating the volume of a vertical prism:

The volume of a right prism is equal to the product of the area of ​​the base multiplied by the height.

In there

• Vis the volume of the prism (unit m3)
• Bis the base area (unit m2)
• his the height of the prism (unit m)

3. Classification of prisms

Regular prism

It is a vertical prism with a regular polygon base. The lateral faces of the prism are all equal rectangles. For example: a regular triangular prism, a regular quadrilateral... then we understand it as a regular prism.

A regular quadrilateral base is called a regular quadrilateral prism.

Triangular prism

• A triangular prism has 5 faces, 9 edges, and 6 vertices.
• The two bases are both triangular and parallel to each other; Each side face is a rectangle;
• The sides are equal;
• The height of a triangular prism is the length of one side.

For example:

The triangular prism ABC.A'B'C' has:

- The bottom base is triangle ABC, the top base is triangle A'B'C';

The side faces are rectangles: AA'B'B, BB'C'C, CC'A'A;

- Edges:

• Base edges: AB, BC, CA, A'B', B'C', C'A'
• Sides: AA', BB', CC';

- Vertices: A, B, C, A', B', C'.

- Height is the length of one side: AA' or BB' or CC'.

Quadrilateral prism

- A quadrilateral prism has 6 faces, 12 edges, and 8 vertices.

- The two base faces are both quadrilaterals and parallel to each other. Each side face is a rectangle.

- The sides are equal.

- The height of a quadrilateral prism is the length of one side.

For example:

Quadrilateral prism ABCD.A'B'C'D' has:

- The bottom base is quadrilateral ABCD, the top base is quadrilateral A'B'C'D';

The side faces are rectangles: AA'B'B, BB'C'C, CC'D'D, DD'A'A;

- Edges:

+ Base edges: AB, BC, CD, DA, A'B', B'C', C'D', D'A'

+ Side edges: AA', BB', CC', DD' are equal.

- Vertices: A, B, C, D, A', B', C', D'.

- Height is the length of one side: AA' or BB' or CC' or DD'.

Note: Rectangular prisms and cubes are also quadrilateral prisms.

Right prism

If a prism has side edges perpendicular to the base, it is called a right prism.

Note:

If the base is a rectangle, the vertical cylinder of the quadrilateral is called a rectangular box.

If a quadrilateral cylinder has 12 sides of length a, then its name is a cube.

Compare the right prism and the regular prism:

4. Example of calculating the volume of a vertical prism

Example 1: 

Given prism ABC.A'B'C' with base ABC being an equilateral triangle with side a = 2 cm and height h = 3 cm. Calculate the volume of this prism?

Prize:

Because the base is an equilateral triangle with side a, the area is:

At this time, the volume of the prism is:

Example 2: 

Exercise 1: Given a vertical box with edges AB = 3a, AD = 2a, AA'= 2a. Calculate the volume of block A'.ACD'

Instruct:

Because the side face ADD'A' is a rectangle, we have:

Example 3 : Given a vertical prism ABC.A'B'C' whose base is an equilateral triangle with side a√3, the angle between it and the base is 60º. Let M be the midpoint of BB'. Calculate the volume of the pyramid M.A'B'C'.

Prize:

Therefore, we can infer that

We have:

Example 4: 

Given a regular quadrilateral prism ABCD.A'B'C'D' with a base edge of a and a face (DBC') with the base ABCD at an angle of 60º. Calculate the volume of prism ABCD.A'B'C'D?

We have: at the center O of square ABCD.

On the other hand therefore

Infer

Also:

Example 5: 

Calculate the volume V of cube ABCD.A'B'C'D', knowing AC'=a√3

Prize:

Let x be the length of the side of the cube.

Consider triangle AA'C right angled at A with:

Therefore, the volume of the cube is V=a^3.

In addition to the formula for calculating the volume of a prism above, you can refer to more articles on the formula for calculating the volume of a solid of revolution , the formula for calculating the area and circumference of a circle ...