Geometry is one of the important branches of mathematics. It studies the spatial properties of figures. One of them is a polyhedron called a prism. This article is devoted to answers to questions about what a prism is and what formulas are used to calculate its basic properties.
Polyhedron - Prism
We begin the article right away with the answer to the question of what is a prism. It is understood as a volumetric polyhedron, which consists of two polygonal and parallel to each other bases and several parallelograms or rectangles. To better imagine what class of figures we are talking about, an example of a pentagonal prism is shown below.
As you can see, two pentagons lie in parallel planes and are equal to each other. Their sides are connected by five rectangles, in this case. From this example it follows that if the base of the figure is a polygon with the number of sides n, then the number of vertices of the prism will be 2 * n, the number of its faces will be n + 2, and the number of edges will be 3 * n. It is easy to show that the quantities of these elements satisfy Euler's theorem:
3 * n = 2 * n + n + 2 - 2.
Above, when an answer was given to the question of what a prism is, we mentioned that the faces connecting the same bases can be parallelograms or rectangles. Note that the latter belong to the class of the former. In addition, it is possible that these faces will be squares. The sides that connect the base of the prism are called lateral. Their number is determined by the number of angles or sides of the polyhedral base.
We briefly mention that the meaning of the word "prism" comes from the Greek language, where it literally means "sawn off". It is easy to understand where such a name came from if you look at the quadrangular wooden prisms in the figure below.
What are the prisms?
Classification of prisms involves consideration of the various characteristics of these figures. So, first of all, the polygonity of the base is taken into account, therefore they talk about triangular, quadrangular and other prisms. Secondly, the shape of the side faces determines whether the figure is straight or whether it will be inclined. In a straight figure, all side faces have four right angles, that is, they are either rectangles or squares. In an inclined figure, these faces are parallelograms.
A special category includes regular prisms. The fact is that their bases are equilateral and equiangular polygons, and the figure itself is straight. These two facts indicate that the sides of such figures are all equal.
Finally, another classification criterion is the convexity or concavity of the base. For example, a concave figure in the form of a five-pointed star is shown above in the figure.
Formulas of the area and volume of the correct figure
Having understood what the correct prism is, we give two main formulas with which you can determine their volume and surface area.
Since the area S of the whole figure is formed from two bases with n sides and n rectangles, then for its calculation, use the following expressions:
S o = n / 4 * ctg (pi / n) * a 2 ;
S = 2 * S o + n * a * h.
Here S o is the area of one base, a is the side of this base, h is the height of the whole figure.
To calculate the volume of the considered type of prisms , the formula should be used:
V = S o * h = n / 4 * ctg (pi / n) * a 2 * h.
The calculation of S and V for the correct figures requires knowledge of only two linear geometric parameters.
Triangular glass prism
What is a prism, we figured it out. This is a perfect object of geometry, it is used to shape many structures and objects. We note only one of the important applications of its form in physics. It is a triangular prism made of glass. Due to its shape, the light incident on it, as a result of dispersion, decomposes into several colors, which allows us to analyze the chemical composition of the emitter.