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