The net of a cone has a circle for its base.

The lateral area of the cone is not so simple.

Do you know what the radius of this larger circle is?
Do you know what the circumference of the lateral area is?

Do you know what the radius of this larger circle is?

The radius of the larger circle is equal to the slant height of the cone.

Do you know what the circumference of the lateral area is?

The circumference of the lateral area is equal to the circumference of the circular base with radius \(r\).

The circumference of the lateral area is \(2 \pi r\).

Did you notice the following?

• The greater the number of sections, the closer the rearrangement looks like a parallelogram.
• The height of the parallelogram is approximately equal to the slant height of the cone.
• The base of the parallelogram is half the circumference of the cone's base, \(\pi r\). 
• The area of the cone's net is the sum of the areas of the circle and the parallelogram.
  \[\begin{align*} SA &\approx A_{\text{Circle}} + A_{\text{Parallelogram}} \\ &\approx \pi r^2 + \pi r \times s \\ &\approx \pi r^2 + \pi rs \end{align*}\]