Prism-Total Surface Area

The surface area of a prism is considered to be the amount of aggregate occupied area by the flat faces of the prism. Its calculation is the total space occupied by all the sides of a particular kind of prism. In another word, finding or calculating the surface area means calculating the total spaces occupied by all the faces of that respective type of prism or can also be calculated by adding the amount of area of all the faces in a 3D plane. In the following, various aspects of the prism such as the total surface area of a prism formula, the total surface area of a triangular prism and its application have been discussed.

The total surface area of a prism formula

There are different kinds of prisms and the formula for calculating the total surface area is also different.  A general is also there to calculate any kind of prism. It has been known that the total surface area of a prism is the sum of all lateral surface area along with two flat surface bases. The lateral area is the region of vertical faces of the prism when the base of a prism faces either up or down. 

That is a lateral Surface area of prism= base parameters*height. 

Therefore, the total surface area of a prism can be obtained by adding lateral surface area of a prism with the area of the two bases. This can further be described as the multiplication of base area with 2 added by lateral surface area. That is, multiplication of base perimeters with height of the prism added by base area * 2.  

The formulas of various types of prisms are different. This is due to the bases of the prism which are different, such as the formula of calculating the surface area of the prism. There are a few steps to calculate the surface area of a prism. In the first step, one should note the given dimensions of the prism. In the second step, one should substitute the dimension area of the prism formula. That is, (2*base area) + (base parameter* height). In the third step, the value of the surface area is obtained and the unit of the same is placed in the end in terms of square units.

The total surface area of a triangular prism 

The total area of all the faces of a triangular prism is its total surface area. It comprises 2 triangular and three rectangular faces. His also includes three triangular faces joined by two triangular faces. The total surface area of a triangular prism is calculated by the sum of the areas of all the faces of the prism. It has three rectangular and two triangular faces. It is also considered to be the lateral face. On the other hand, triangular faces are called bases. If the bases are placed horizontally, they can be considered as the top and bottom faces of the prism respectively. The surface area of a triangular prism is demonstrated in square units.

The formula for calculating the surface area of a triangular prism is; 

Surface area= (perimeters of the base*length of the prism) + (2 * base area) = (S1+S2+S3)L+ bh.

Where, 

L depicts the length of the prism

S1, S2, and S3 demonstrates the three edges or sides of the base triangle

b is the bottom edge of the base triangle

bh is the combined area of two triangular faces.

h stands for the height of the base triangle

Application of surface area of a triangular prism

There are multiple applications of a triangular prism. For example, a telescope uses the triangular prism in determining the accuracy of the distance using the reflections of light. It helps reduce the wavelength to be observable by the human eye. Apart from that, triangular prisms have also been used in microscopes for the same purpose as a telescope. In the telescope, the wavelength is shortened by the use of a triangular prism. In the microscope, the opposite side of the triangular prism is used to broaden the short wavelength. In the periscopes, two triangular prisms are used one place in a telescoping manner and the other one using microscopes. That is the first one reduces the wavelength and the second increases the wavelength for the human eyes. It is also used in medicine. A triangular prism is used to study the reaction or response of the human eyes to light exposure. The use of light reflecting and refracting prisms are prominently used in optical research, architecture, RFID, particle research and so on. In architecture, triangular prisms are used for calculating and designing the buildings or infrastructure in a precise manner. In the cold region, architectural work is quite striving for engineers. Here, triangular prisms are used for standard designing of the construction due to the steep slopes covered by a thick layer of snow.

Conclusion

In the calculation of the surface area of a triangular prism, various aspects have been discussed. Firstly, the calculation of the surface area of a prism has been demonstrated using the lateral surface area of a prism. After that, a triangular prism has been considered. The calculation of the triangle prism along with various applications has also been depicted with specific areas such as architecture, physics, and medical and so on. Modern technologies have also been described for the application of triangular prisms such as RFID. Geographical aspects of the construction and the use of triangular prisms have also been described.