In physics, a triangular prism made of glass is often used to study the spectrum of white light, since it can decompose it into separate components. In this article, we consider the formula for the volume of a direct triangular prism.
What is a triangular prism?
Before giving the formula for the volume of a triangular prism, we consider the properties of this figure.
To obtain this type of prism, it is necessary to take a triangle of arbitrary shape and parallel to itself transfer it to a certain distance. The vertices of the triangle in the initial and final position should be connected by straight segments. The resulting volumetric figure is called a triangular prism. It has five sides. Two of them are called bases: they are parallel and equal to each other. The bases of the prism under consideration are triangles. The three remaining sides are parallelograms.
In addition to the sides, the prism under consideration is characterized by six vertices (three for each base) and nine edges (6 edges lie in the planes of the bases and 3 edges are formed by the intersection of the sides). If the side ribs are perpendicular to the bases, then such a prism is called rectangular.
The difference of a triangular prism from all other figures of this class is that it is always convex (four-, five-, ..., n-angle prisms can also be concave).
A regular triangular prism is a rectangular figure, at the base of which lies an equilateral triangle.
Volume of a triangular prism of a general type
How to find the volume of a triangular prism? The formula in general form is similar to that for a prism of any kind. She has the following mathematical notation:
V = S o * h
Here h is the height of the figure, that is, the distance between its bases, S o is the area of the triangle.
The value of S o can be found if some parameters are known for the triangle, for example, one side and two angles, or two sides and one corner. The area of a triangle is equal to half the product of its height by the length of the side by which this height is lowered.
As for the height h of the figure, it is easiest to find for a rectangular prism. In the latter case, h coincides with the length of the side rib.
Volume of a regular triangular prism
The general formula for the volume of a triangular prism, which is given in the previous section of the article, can be used to calculate the corresponding value for a regular triangular prism. Since an equilateral triangle lies at its base, its area is equal to:
S o = √3 / 4 * a 2
Everyone can get this formula if he remembers that in an equilateral triangle all angles are equal to each other and amount to 60 o . Here, the symbol a is the length of the side of the triangle.
Height h is the length of the rib. It has nothing to do with the base of the correct prism and can take arbitrary values. As a result, the formula for the volume of a triangular prism of the correct form looks like this:
V = √3 / 4 * a 2 * h
Having calculated the root, we can rewrite this formula as follows:
V = 0.433 * a 2 * h
Thus, in order to find the volume of a regular prism with a triangular base, it is necessary to square the side of the base, multiply this value by height and multiply the resulting value by 0.433.