A triangular prism is one of the frequent volumetric geometric shapes that we meet in our life. For example, on sale you can find key chains and watches in the shape of it. In physics, this figure made of glass is used to study the spectrum of light. In this article, we discuss the question regarding the development of a triangular prism.
What is a triangular prism?
Consider this figure from a geometric point of view. To get it, you need to take a triangle having arbitrary lengths of sides, 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 figure shows that it is formed by 5 faces. Two identical triangular sides are called bases, three sides represented by parallelograms are called lateral. At this prism, there are 6 vertices and 9 edges, of which 6 lie in the planes of parallel bases.
Regular triangular prism
The triangular prism of the general type was considered above. It will be called correct if the following two prerequisites are met:
- Its base should be a regular triangle, that is, all its angles and sides should be the same (equilateral).
- The angle between each side face and the base should be straight, that is, 90 o .
The photo above shows the figure in question.
For the correct triangular prism, it is convenient to carry out calculations of the length of its diagonals and the height, volume and surface area.
Scan of a regular triangular prism
Take the correct prism shown in the previous figure and mentally perform the following operations for it:
- First, cut two edges of the upper base, which are closest to us. Bend the base up.
- We perform the operations of point 1 for the lower base, only bend it down.
- We cut the figure along the nearest side edge. Bend left and right two side faces (two rectangles).
As a result, we get a scan of a triangular prism, which is presented below.
This scan is conveniently used to calculate the lateral surface area and the base of the figure. If the length of the side rib is equal to c, and the length of the side of the triangle is equal to a, then for the area of two bases, we can write the formula
S o = a 2 * √3 / 2.
The lateral surface area will be equal to three areas of identical rectangles, that is:
S b = 3 * a * c.
Then the total surface area will be equal to the sum of S o and S b .