Introduction about prisms:

Triangular prisms are three sided prism. The flat surface is called faces of the triangular prism. It has six vertices. Formula to find the surface area and volume of the prism is given below.

 

 

Surface area and volume of right triangular prism:

Total surface area T.S.A = (P x h + 2 A) sq. units              

                        P = perimeter of base (a + b + c)

                        h = height of the prism

                        A = Area of the base

Volume of the prism (V) = ½ Al cubic units

Rectangular prisms are one type of the prism. It has four sides. It has eight vertices. Formula to find the surface area and volume of the prism is given below.

 Surface area and volume of rectangular prism:

           

            Total surface area of rectangular prism

                                    = 2 (length x breadth + breadth x width + length x height)

                                    =2(lb + bh+ lh) square units

            Volume of the rectangular prism (V) = l x w h cubic units

 

Right triangular prisms- Example problem

 

1. The base of a prism is a right angled triangle of side 4 cm, 3cm and 5 cm. its length is 10 cm. find total surface area and volume of prism.

Solution:

Given:

Let us take the base of the right triangular prism = 4 cm

                                                       Height (h) =3 cm

                                        Length of the prism = 10 cm

 

Formula:

            Total surface area T.S.A = (P x l + 2 A) sq. units

 

            Perimeter (p) = a + b + c

 

                                  = 4 + 3 + 5

                                  = 12 cm

            Area of the base (A) = ½ (base x height)

                                              = ½ (4 x 3)

                                              = 12/2

                                              = 6 cm2

Substitute in the formula,

                        T.S.A = (12 x 10 + 2 x 6)

                                  = 120 + 12

                                  = 132 cm3

Total surface area T.S.A = 132 cm2

 

Volume of the prism (V) = ½ Al cubic units

                                            = ½ (6 x 10)

                                           =60 / 2

      Volume of the prism = 30 cubic units

 

Rectangular prisms - Example problem

 

1.      Find the lateral surface area and total surface area of a rectangular whose length is 10 cm, width 8cm and height 6cm.

Solution:

Given:

                              Length (l) = 10cm

                             Width (w) = 8 cm

                           Height (h) = 6 cm

Total surface area of rectangular prism =2(wh + lw+ lh) square units

                                                               = 2(8 x 6+ 10 x 8 + 10 x 6)

                                                               = 2 (48 + 80 + 60)

                                                               = 2 (188)

                                                               = 376

Total surface area of rectangular prism = 376 cm2

            Volume of the rectangular prism (V) = l x w x h cubic units

                                                                           = 10 x 8 x 6

                                                                           = 80 x 6

                                                                           = 480 cm3