Quadrilateral Prism Shape

In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same (source-Wikipedia). If the prism has four sides then it is called quadrilateral prism. in this article we shall discus about some quadrilateral prism.

Quadrilateral prim shapes:

Cube:

It is one type of quadrilateral prism. Its all dimensions are equal in measure (all side are equal).it has eight vertices. The shape of the cube is shown in below.
Formula for Volume of the cube V= a3 cubic units
Where,
            V = volume of the cube
 a =side length (or edge) of the cube.
Formula for surface area of the cube (A) = 6 a² square units

Rectangle prism:

It is one type of quadrilateral prism. The shape of the cube is shown in below.
Volume of rectangular solid (V) = length x width x height Cubic units
     = l x w x h cubic unit.
Total surface area of rectangular prism
                                    = 2 (length x breadth + breadth x width + length x height)
                                    =2(lb + bh+ lh) square units

Trapezoidal prism:

It is one type of quadrilateral prism.it has one set of parallel sides. The shape of the trapezoidal prism is shown in the figure.
Volume of trapezoidal prism = l x area of the base cubic units
                                                       l – Length of trapezoidal prism
                              Area of the base= 1/2 x (a + b) x h square units
                                                       a and b are length of parallel sides.
                                                       h – Height

Quadrilateral prism shape - Example problems:

1. Find the volume and surface area of the cube whose side length is 17 cm.
Solution:
            Given:
                        Side length (a) = 17 cm
Formula:
            Volume of the cube V= a³ cubic units
                                                = 17³
                                                = 17 x 17 x 17
                                                = 4913 cm³
            Surface area of the cube (A) = 6 a² square units
                                                          = 6 x 17²
                                                          = 6 x 289
                                                          = 1734 cm²

2. Find the lateral surface area and total surface area of a rectangular whose length is 6 cm, width 3cm and height 6cm.
Solution:
Given:
                              Length (l) = 6 cm
                         Width (w) = 3 cm
                           Height (h) = 6 cm
Total surface area of rectangular prism =2(wh + lw+ lh) square units
                                                               = 2(3 x 6+ 6 x 3 +6 x 6)
                                                               = 2 (18 + 18 + 36)
                                                               = 2 (72)
                                                               = 144
Total surface area of rectangular prism = 144 cm²
            Volume of the rectangular prism (V) = l x w x h cubic units
                                                                           = 6 x 3 x 6
                                                                           = 108
                                                                           = 108 cm³
3.figure out the volume trapezoidal prism whose length 14 cm, height 5cm, length of parallel sides a=7 cm and b=4cm.
Solution:
Given:
                  Length (l) = 20 cm
                  Height (h) = 5 cm
                  Parallel sides a=7 cm and b=4 cm
Formula:
Volume of trapezoidal prism = l x area of the base cubic units

Area of the base:
Area of the base= 1/2 x (a + b) x h
                                                   = 1/2x (7 + 4) x 5
                                                   =1/2 x 11 x 5
                                                     = 27.5 cm²
Volume of trapezoidal prism = 20 x 27.5
                                                  = 550

Volume of trapezoidal prism = 550 cm³