Earlier, we saw the area of shapes is calculated – in general – by multiplying the length and breadth of the shape. Shapes, such as triangles, squares, etc, are two-dimensional, i.e., they lie in a plane. However when objects are three-dimensional, i.e., they cannot be represented in a plane, they are called solids.

Some examples of solids are a cube, rectangular prism, triangular prism, cylinder and cone, as shown below –

The surface area of a solid with plane faces is the sum of the areas of its faces.

The calculation of a surface area can be made easier by knowing whether the number of faces have the same area. It is also necessary to consider whether the figure is open or closed, such as a swimming pool.

Calculating surface area is important in many trades like painting, decorating, tiling, layering, etc. Tradespeople need to calculate (or estimate) the total surface area involved in a job so that they can decide on the fee to be charged, and the quantity of materials needed.

For example, a painter is required to quote for a job to paint a room. He will first find the dimensions of the room, then work out the area of each wall to get the total ‘surface area’ of the walls to be painted. He may then be required to work out the amount of paint to purchase, the time required to complete the job, and hence his cost.

We now look at calculating the surface areas of different solids: