How do you find the surface area of a rectangular prism with dimensions 4 cm, 5 cm, and 6 cm?

To find the surface area of a rectangular prism, calculate the sum of the areas of all six faces.

A rectangular prism has six faces, and each face is a rectangle. The dimensions of the prism are given as 4 cm, 5 cm, and 6 cm. To find the surface area, you need to calculate the area of each pair of opposite faces and then sum them up.

First, identify the three pairs of opposite faces:
1. The faces with dimensions 4 cm by 5 cm.
2. The faces with dimensions 4 cm by 6 cm.
3. The faces with dimensions 5 cm by 6 cm.

Next, calculate the area of each pair of faces:
1. The area of one face with dimensions 4 cm by 5 cm is \(4 \times 5 = 20\) square centimetres. Since there are two such faces, their total area is \(2 \times 20 = 40\) square centimetres.
2. The area of one face with dimensions 4 cm by 6 cm is \(4 \times 6 = 24\) square centimetres. For two such faces, the total area is \(2 \times 24 = 48\) square centimetres.
3. The area of one face with dimensions 5 cm by 6 cm is \(5 \times 6 = 30\) square centimetres. For two such faces, the total area is \(2 \times 30 = 60\) square centimetres.

Finally, add the areas of all the faces together to find the total surface area:
\[40 + 48 + 60 = 148\] square centimetres.

So, the surface area of the rectangular prism is 148 square centimetres.