Prisms are solids with plane faces. As we saw earlier, the surface area of prisms, i.e. the surface area of a solid with plane faces is the sum of the area of its faces.

We will first look at calculating the surface area of a cube, and then that of a rectangular prism and a triangular prism.

**Surface area of a cube**

A cube is a six-sided solid with a uniform cross-section; and the cross-section of a cube is a square.

Let us look at a cube with side 2 cm. ‘Opening up’ this cube will produce a net. A net is a flat diagram that contains the faces of a solid shape. The faces are arranged so that the diagram could be folded to form that solid (in this case, a cube). Drawing the net of a prism can help with calculating the surface area.

So to calculate the surface area of this cube, we first calculate the area of one side.

Area of one side = 2 x 2 = 4 cm^{2}

Since there are six sides to a cube, Surface area of a cube = 6 x area of one face

= 6 x 4

= 24 cm^{2}

In general, the formula to calculate the surface area of a cube, given side a, is –

Surface area of a cube = 6a^{2}

**Example 1**** ****:** What is the surface area of a cube with side 5 mm?

Let us first do a net diagram for this cube –

Area of one face = 5 x 5 = 25 mm^{2}

Surface area of the cube = 6 x area of one face

= 6 x 25

= 150 mm^{2}

We can also calculate the surface area using the formula 6a^{2}

Surface area = 6 x 5^{2}

= 150 mm^{2}

**Example 2**** ****:** What is the surface area of a cube with side 7.5 m?

Surface area of a cube = 6a^{2}

= 6 x 7.5^{2}

= 6 x 56.25

= 337.5 m^{2}

Here are some more examples of surface area of prisms.