Let us look at some examples of surface area of prisms.

Example 1 : What is the surface area of this cube?

There are two ways to calculate the surface area of a cube.

(i) Surface area  =  6a²   (a = side of a cube)

=  6 x 5²

=  6 x 25

=  150 cm²

(ii) Area of one side = 5 x 5 = 25 cm²

Since there are 6 sides, surface area = 6 x 25 = 150 cm²

 

Example 2 : Calculate the surface area of this rectangular prism.

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

=  (6 x 2 x 2) + (2 x 4 x 2) + (6 x 4 x 2)

=  24 + 16 + 48

=  88 cm²

 

Example 3 : Find the surface area of a cube with side length of 7 mm.

Surface area  =  6a²

=  6 x 7²

=  6 x 49

=  249 mm²

 

Example 4 : Calculate the area of the triangular prism shown here.

There are 5 faces in this prism – 2 triangular faces of equal area and 3 rectangles.

The triangular face is an isosceles triangle. Its area  =  x b x h

=   x 6 x 4

=  12 cm²

So, area of two triangular faces = 24 cm²

Area of the 3 rectangular faces = area of left face + area of right face + area of back face

=  (12 x 5) + (12 x 5) + (12 x 6)

=  60 + 60 + 72

=  192 cm²

So the total area of the triangular prism = 12 + 192 = 204 cm²

 

Example 5 : Find the side length of a cube whose surface area is 96 cm².

Surface area of cube  =  6a²

96  =  6a²

a²  =  36

a  =  6

So the side length of the cube is 6 cm.

 

Example 6 : A rectangular prism has a surface area of 188 cm². Find the length of the prism if it is 4 cm wide and 6 cm high.

Surface area of rectangular prism = 2 (lb + bh + lh)

188  =  2 (lx4 + 4×6 + lx6)

94  =  4l + 24 + 6l

10l  =  94 – 24

10l  =  70

l  =  7 cm

So the length of the rectangular prism is 7 cm.

 

Example 7 : What is the surface area of the triangular prism shown here?

Surface area = (area of triangular faces x 2) + (area of bottom face) + (area of front face) + (area of back face)

=  (2 x x 4)  +  (6 x 4)  +  (6 x 5)  +  (6 x 3)

=  12 + 24 + 30 + 18

=  84 cm²