Introduction:

 In this following article we are going too see in detail about the vertices of hexagonal prism in detail and the ways of using it to determine the various relations using these vertices. The vertices are the points where the two sides of a polygon meet. By calculating the distance between the two vertices of a hexagonal prism we can find the side distance. This can be used to find the volume, surface area of the hexagonal prism.

 


 

Vertices of a hexagonal prism:

 

  • The hexagonal prism has two bases in total. Each base will be having 6 vertices. So a hexagonal prism will have,

       2 x 6 = 12 vertices.

  • Also it will have 6 edges in bottom base, 6 in top base, and 6 lateral edges.
  • The vertices of the hexagonal prism will have the vertices of the bases with any of the coordinate value same. So by calculating the distance between the corresponding vertices of the two sides we can calculate the height of the hexagonal prism.
  • By these methods we calculate the height and side of a hexagonal prism. Now it becomes easy for us to calculate the volume and the surface area of the prism.
  • In coordinate geometry the formula for finding the distance between two points (x1,y1),(x2,y2) is given by,

       d = √[(x2-x1)2+(y2-y1)2]

  • This formula can be used in calculating the distance between the two vertices in the prism.

 

Example problems on vertices of a hexagonal prism:

 

1. Given the two consecutive vertices of a hexagonal prism base are (2,3)(3,4). The corresponding vertices for another base of a hexagonal prism are (2,8),(3,9). Calculate the volume of the prism.

Solution:

Distance d = √ [(x2-x1)2+ (y2-y1)2]

Side of the prism a = √ [(3-2)2+ (4-3)2]

                            = √ (1+1)

                            = √ (2)

Height of the prism h = √ [(x2-x1)2+ (y2-y1)2]

                                = √ [(2-2)2+ (8-3)2]

                               = √ (5) 2

                               = 5.

Volume = 3√3 a2/ h

           = 3√3 (√2)2/ 5

           = 3√3 (2)/ 5

           = (6√3)/ 5

 

Exercise problems on vertices of a hexagonal prism:

1. Given the two consecutive vertices of a hexagonal prism base are (3,4)(5,7). The corresponding vertices for another base of a hexagonal prism are (3, 10),(5,13). Calculate the volume of the prism.

Answer: 13√3/ 2.