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 answering the questions, what is a prism and what formulas are used to calculate its main properties.
Polyhedron - prism
Let's start the article right away with the answer to the question, what is a prism. It is understood as a three-dimensional polyhedron, which consists of two polygonal and parallel bases and several parallelograms or rectangles. To better understand 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 n sides, then the number of vertices of the prism will be 2n, the number of its faces will be n + 2, and the number of edges will be 3n. It is easy to show thatthe quantities of these elements satisfy Euler's theorem:
3n=2n + n + 2 - 2.
Above, when the 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 bases of the prism are called lateral. Their number is determined by the number of corners or sides of the polyhedral base.
Briefly mention that the meaning of the word "prism" comes from the Greek language, where it literally meant "sawed off". It is easy to understand where this name comes from if you look at the quadrangular wooden prisms in the figure below.
What are prisms?
Classification of prisms involves considering the various characteristics of these figures. So, first of all, the polygonality of the base is taken into account, so they talk about triangular, quadrangular and other prisms. Secondly, the shape of the side faces determines whether the figure is straight or slanted. 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.
Regular prisms belong to a special category. The fact is that their bases are equilateral and equiangular polygons, and the figure itself is a straight line. These twothe facts say that the sides of such figures are all equal to each other.
Finally, another classification criterion is the convexity or concavity of the base. For example, the concave five-pointed star is shown above.
Formulas for the area and volume of a regular figure
Having figured out what a regular prism is, here are 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, the following expressions should be used to calculate it:
So=n / 4ctg(pi / n)a2;
S=2So+ nah.
Here So- one base is the area, a is the side of this base, h is the height of the whole figure.
To calculate the volume of the considered type of prism, use the formula:
V=So h=n / 4ctg(pi / n)a2 h.
Calculation of S and V for regular 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 give shape to many structures and objects. Let us note only one of the important applications of its form in physics. This is a triangular prism made of glass. Due to its shape, the light falling on it, as a result of dispersion, decomposes into several colors, which allowsanalyze the chemical composition of the emitter.
