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 = 6a^{2} (a = side of a cube)

= 6 x 5^{2}

= 6 x 25

= 150 cm^{2}

(ii) Area of one side = 5 x 5 = 25 cm^{2}

Since there are 6 sides, surface area = 6 x 25 = 150 cm^{2}

**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 cm^{2}

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

Surface area = 6a^{2}

= 6 x 7^{2}

= 6 x 49

= 249 mm^{2}

**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 cm^{2}

So, area of two triangular faces = 24 cm^{2}

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 cm^{2}

So the total area of the triangular prism = 12 + 192 = 204 cm^{2}

**Example 5**** ****:** Find the side length of a cube whose surface area is 96 cm^{2}.

Surface area of cube = 6a^{2}

96 = 6a^{2}

a^{2} = 36

a = 6

So the side length of the cube is 6 cm.

**Example 6**** ****:** A rectangular prism has a surface area of 188 cm^{2}. 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 cm^{2}