In this lesson, we will look at using nets to calculate the surface area of a cube, rectangular prism or cuboid, triangular prism, cylinder, pyramid and cone.

A net is a pattern made when the surface of a three-dimensional figure or solid is laid out flat showing each face of the figure. It is then possible to use the net to calculate the surface area of the solid.

A cube is a three-dimensional figure with six matching square faces.

The following nets can be folded along the dotted lines to form a cube.

For example, ifthe length of one side of the cube 3 units then the area of one its face is 3 × 3 = 9 units^{2}. From the net, we can see that there are six equal faces and so we get the total surface area is 6 × 9 = 54 units^{2}

Surface Area of a Rectangular Prism using Nets

A rectangular prism or cuboid is formed by folding a net as shown:

We can see from the net that there are two rectangles with dimensions 3 cm by 6 cm, two rectangles with dimensions 2 cm by 6 cm and two rectangles with dimensions 2 cm by 3 cm. The total surface area is then

2 × 3 × 6 + 2 × 2 × 6 + 2 × 2 × 3 = 72 cm^{2}

This video shows how to find the surface area of a rectangular prism when its net is given.

This video shows how to find the surface area of a rectangular prism using nets.

Surface Area of a Triangular Prism using Nets

This video shows how to find the surface area of a triangular prism using nets.

This video shows how to calculate the surface area of a triangular prism by first drawing a net for the prism.

Surface Area of a Cylinder using Nets

This video provides a specific example of how to find the surface area of a cylinder by drawing the net.

Surface Area of a Pyramid using Nets

This video shows how to find the surface area of a pyramid and a cylinder by drawing the nets.

Surface Area of a Hexagonal Prism using Nets

This video shows how to find the surface area of a hexagonal prism by drawing a net.

Surface Area of a Cone

Surface Area and volume of a right circular cone.

In this lesson you will learn to determine whether to find area, surface area, or volume in a given situation by thinking about what units are needed.

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