# Regular ocatagons, what are the mathematical properties of a regular octagon (math facts)

There are many mathematical properties of a regular octagon:

1) A regular octagon has 8 equal side lengths.

2) A regular octagon has 8 equal angles.

3) A regular octagon has 8 lines of reflectional symmetry.

4) An octagon has order 8 rotational symmetry. This means that the shape can be turned 8 times onto itself in a full 180⁰

5) The exterior angle of a regular octagon is 45⁰. This is calculated by dividing 360⁰ by the amount of angles.

6) The interior angle of a regular octagon is 135⁰. This can be found by subtraction the exterior angle from 180⁰ (180 – 45 = 135).

7) The centre angle of a regular octagon is 45⁰. The centre angle can be found by dividing 360 by the amount of sides.

8) The sum of interior angles of a regular octagon is 180 × 6 = 1080⁰ (this is the total of all the interior angles)

9) The number of diagonals that can be drawn inside a regular octagon is 20.

10) The area of a regular octagon can be found by using the following formula:

A = 2(1+√2)s²

Note: s stands for side length.

So for example, if you were to calculate the area of a regular octagon that has side length equal to 7 inches, then the area can be found by plugging in s = 7 into the formula above:

A = 2(1+√2)7²

A = 2 × (1+√2) × 49

A = 98 × (1+√2)

A = 237 squared inches rounded to 3 significant figures.

In the non mathematical world, you will find regular octagons on road signs (stop signs) and coins. Also umbrellas often come in the shape of a regular octagon.

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