Regular triangular prism, its development and surface area

2024 Author: Angel Austin | [email protected]. Last modified: 2023-12-17 05:14

The triangular prism is one of the most common volumetric geometric shapes that we meet in our lives. For example, on sale you can find key chains and watches in the form of it. In physics, this figure made of glass is used to study the spectrum of light. In this article, we will cover the issue regarding the development of a triangular prism.

What is a triangular prism

Let's consider this figure from a geometric point of view. To get it, you should take a triangle with arbitrary side lengths, and parallel to itself, transfer it in space to some vector. After that, it is necessary to connect the same vertices of the original triangle and the triangle obtained by the transfer. We got a triangular prism. The photo below shows one example of this figure.

The picture shows that it is formed by 5 faces. Two identical triangular sides are called bases, three sides represented by parallelograms are called lateral. This prismyou can count 6 vertices and 9 edges, 6 of which lie in the planes of parallel bases.

Regular triangular prism

A triangular prism of a general type was considered above. It will be called correct if the following two mandatory conditions are met:

1. Its base must represent a regular triangle, that is, all its angles and sides must be the same (equilateral).
2. The angle between each side face and the base must be straight, that is, 90^o.

The photo above shows the figure in question.

For a regular triangular prism, it is convenient to calculate the length of its diagonals and height, volume and surface area.

Sweep of a regular triangular prism

Take the correct prism shown in the previous figure and mentally carry out the following operations for it:

1. Let's first cut the two edges of the upper base, which are closest to us. Fold the base up.
2. We will do the operations of point 1 for the lower base, just bend it down.
3. Let's cut the figure along the nearest side edge. Bend left and right two side faces (two rectangles).

As a result, we will get a triangular prism scan, which is presented below.

This sweep is convenient to use to calculate the area of the lateral surface and bases of the figure. If the length of the side edge is c and the lengthside of the triangle is equal to a, then for the area of two bases, you can write the formula:

S_o=a²√3/2.

The area of the lateral surface will be equal to three areas of identical rectangles, that is:

S_b=3ac.

Then the total surface area will be equal to the sum of S_oand S_b.