A prism is a polygon with two parallel and equal base faces and a parallelogram on the sides.
Comment:
- The sides of the prism are equal and parallel to each other
- The sides are parallelograms
- The two bases of a prism are two equal polygons
Formula to calculate the volume of a prism (V prism), what is the formula to calculate the volume of a vertical prism? Please refer to the article below.
1. Volume of a vertical prism
Formula for calculating the volume of a vertical prism:
The volume of a vertical prism is equal to the product of the area of the base multiplied by the height.
In there
V
is the volume of the prism (unit m3)B
is the base area (unit m2)h
is the height of the prism (unit m)
3. Classification of prisms
Regular prismatic shape
It is a vertical prism with a base that is a regular polygon. The side faces of the prism are all equal rectangles. For example: equilateral triangular prisms, equilateral quadrilaterals… then we understand them as equilateral prisms
A base surface that is a regular quadrilateral is called a regular quadrilateral prism.
Triangular prism shape
- A triangular prism has 5 faces, 9 edges, and 6 vertices.
- The two bases are triangular and parallel to each other; Each side is rectangular;
- The sides are equal;
- The height of a triangular prism is the side length.
For example:
The triangular prism ABC.A'B'C' has:
– The lower base is triangle ABC, the upper base is triangle A'B'C';
The sides are rectangles: AA'B'B, BB'C'C, CC'A'A;
– Edges:
- Bottom edge: AB, BC, CA, A'B', B'C', C'A'
- Side: AA', BB', CC';
– Vertices: A, B, C, A', B', C'.
– Height is the length of one side: AA' or BB' or CC'.
Quadrilateral vertical prism
– A quadrilateral prism has 6 faces, 12 edges, and 8 vertices.
– The two base faces are quadrilaterals and parallel to each other. Each side is rectangular.
– 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 lower base is quadrilateral ABCD, the upper base is quadrilateral A'B'C'D';
The sides are rectangles: AA'B'B, BB'C'C, CC'D'D, DD'A'A;
– Edges:
+ Bottom edge: AB, BC, CD, DA, A'B', B'C', C'D', D'A'
+ The sides: 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: Rectangles and cubes are also quadrilateral prisms.
Vertical prism
If a prism has side edges perpendicular to the base surface, it is called a vertical prism.
Note:
If the base surface is rectangular, the vertical cylinder of the quadrilateral has another name, a rectangular box.
If a quadrilateral cylinder has 12 sides of length a, then its name is a cube.
Compare a vertical prism and a regular prism:
DEFINE: | NATURE |
+ A vertical prism is a prism with one side perpendicular to the base |
+ The sides of a vertical prism are rectangular + The prismatic side faces stand perpendicular to the bottom surface + Height is the side |
+ A regular prism is a vertical prism whose base is a regular polygon |
+ The side faces of the prism are all equal rectangles + Height is the side |
4. Example of calculating the volume of a vertical prism
Example 1:
Let the prism ABC.A'B'C' have base ABC as 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 point, the volume of the prism is:
Example 2:
Exercise 1: Given a vertical box with sides AB = 3a, AD = 2a, AA'= 2a. Calculate the volume of block A'.ACD'
Instruct:
Because the side ADD'A' is rectangular, we have:
Example 3: Let the right prism ABC.A'B'C' have the base as an equilateral triangle of side a√3, the middle and base angles are 60º. Call M the midpoint of BB'. Calculate the volume of the pyramid M.A'B'C'.
Prize:
Due should infer
We have:
Example 4:
Given a regular quadrilateral prism ABCD.A'B'C'D' with base edge equal to a and face (DBC') with base ABCD at an angle of 60º. Calculate the volume of prism ABCD.A'B'C'D?
We have: at center O of square ABCD.
On the other hand therefore
Inferred
Again there is:
Example 5:
Calculate the volume V of cube ABCD.A'B'C'D', knowing AC'=a√3
Prize:
Let x be the side length 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 the article about the formula for calculating the volume of a circular block, the formula for calculating the area and circumference of a circle…