A regular octagon has side lengths of 9 units. Each side of the octagon is

increased by 27 units. What are the perimeters of the original octagon

and new octagon?

The perimeter of the original octagon is:

72 units.

The perimeter of the new octagon is:

288 units.

Step-by-step explanation:

When it is mentioned that an octagon is regular, it means that all its sides are equal, therefore, each side of the original octagon has a length of 9 units, considering the formula of the octagon's perimeter:

Perimeter of an octagon = 8 * length.

By replacing you get:

Perimeter of the original octagon = 8 * 9 = 72 units.

For the new octagon, it is mentioned that each side increases by 27 units, therefore:

New length = 27 + 9 = 36 units.

Applying the formula of perimeter of an octagon with the new values we obtain:

Perimeter of the new octagon = 8 * 36 = 288 units.