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# Octagon calculator - diagonals, area, perimeter, sides

Octagon calculator will help you calculate the long diagonal of the octagon, the medium diagonal of the octagon, the shorter diagonal of the octagon, the side length, height, area of the octagon, circumference and radius of the circumscribed circle and the radius of the circle inscribed in the regular octagon.

## Longer diagonal octagon

$$P_{d}=a \cdot \sqrt{4+2\cdot \sqrt{2}}$$

## Medium diagonal octagon

$$P_{s}=a \cdot (1 + \sqrt{2})$$

## Shorter diagonal octagon

$$P_{k}=a \cdot \sqrt{(2 + \sqrt{2})}$$

## Height octagon

$$h=a \cdot (1 + \sqrt{2}) = P_{k} = 2 \cdot r$$

## Area octagon

$$S=2\cdot a^{2}\cdot \cot(\frac {\pi }{8}) = 2\cdot(1+{\sqrt {2}})\cdot a^{2}$$

## Perimeter octagon

$$L=8\cdot a$$

## Radius of a circle inscribed in a regular octagon

$$r={\frac {a\cdot (1+{\sqrt {2}})}{2}}$$

## Radius of the circle circumscribed on the octagon

$$R=a\cdot {\sqrt{\frac {2+{\sqrt {2}}}{2}}}$$

Octagon - information

Octagon - a polygon with eight sides and eight interior angles. The sum of the angle measures in any octagon is 1080 °.

A regular octagon is a regular polygon with eight equal sides and 135° internal angles.

It has the following properties ( a , is the length of the side of the octagon):
1. Its every inside angle has a measure $$135^{\circ }$$
2. Radius of the circumscribed circle: $$R=a\cdot {\sqrt{\frac {2+{\sqrt {2}}}{2}}}$$
3. Radius of the inscribed circle: $$r={\frac {a\cdot (1+{\sqrt {2}})}{2}}$$
4. Area of a regular octagon: $$S=2\cdot a^{2}\cdot \cot(\frac {\pi }{8}) = 2\cdot(1+{\sqrt {2}})\cdot a^{2}$$
5. Perimeter of a regular octagon has length: $$L=8\cdot a$$
6. Longer diagonal of a regular octagon has length: $$P_{d}=a \cdot \sqrt{4+2\cdot \sqrt{2}}$$
7. Medium diagonal of a regular octagon has length: $$P_{s}=a \cdot (1 + \sqrt{2})$$
8. Shorter diagonal of a regular octagon has length: $$P_{k}=a \cdot \sqrt{(2 + \sqrt{2})}$$
9. Height of a regular octagon: $$h=a \cdot (1 + \sqrt{2}) = P_{k} = 2 \cdot r$$
10. The number of diagonals of a regular octagon is 20, of which: 4 are long diagonals (Pd), 8 are medium diagonals (Ps) and 8 are short diagonals (Pk)

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