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# Heptagon calculator - diagonals, area, perimeter, sides

Heptagon calculator will help you calculate the long diagonal of the heptagon, the short diagonal of the heptagon, the side length, heights, area of the heptagon, the radius of the circumscribed circle and the radius of the circle inscribed in a regular heptagon.

## Longer diagonal of a regular heptagon calculator

$$P_{d}=\frac{a}{2\cdot \sin(\frac{\frac{\pi}{2}}{7})} =\frac{a}{2\cdot \sin(\frac{\pi}{14})}$$ ## Shorter diagonal of a regular heptagon calculator

$$P_{k}=a\cdot 2\cdot \cos(\frac{\pi}{7})$$ ## Height of a regular heptagon calculator

$$h=\frac{a}{2\cdot \tan(\frac{\frac{\pi}{2}}{7})} =\frac{a}{2\cdot \tan(\frac{\pi}{14})}$$ ## Area of a regular heptagon calculator

$$S=\frac{7}{4}\cdot a^2\cdot \cot(\frac{\pi}{7})$$ ## Perimeter of a regular heptagon calculator

$$L= 7\cdot a$$ ## Radius of the circle circumscribed on a regular heptagon calculator

$$R=\frac{a}{2\cdot \sin(\frac{\pi}{7})}$$ ## The radius of the circle inscribed in a regular heptagon calculator

$$r=\frac{a}{2\cdot \tan(\frac{\pi}{7})}$$ Heptagon- information

Heptagon - a polygon with seven sides and seven interior angles. The sum of the angle measures in any heptagon is 900°.

A regular heptagon is a regular polygon with seven equal sides and internal angles of measurement $${128{\tfrac {4}{7}}}^{\circ }\approx 128{,}57^{\circ }}$$. Impossible to construct with a compass and a ruler. It has twice as many diagonals as the sides. It has the following properties (a, is the length of a side of a heptagon):
1. Its every inside angle has a measure $${128{\tfrac {4}{7}}}^{\circ }\approx 128{,}57^{\circ }}$$
2. The center angle of the circumscribed circle, based on the side, has a measure $${\frac {360^{\circ }}{7}}\approx 51{,}43^{\circ }}$$
3. Radius of the circumcircle (circumscribed circle) : $$R=\frac{a}{2\cdot \sin(\frac{\pi}{7})}$$
4. Radius of the inscribed circle: $$r=\frac{a}{2\cdot \tan(\frac{\pi}{7})}$$
5. Area of a regular heptagon: $$S=\frac{7}{4}\cdot a^2\cdot \cot(\frac{\pi}{7})$$
6. Perimeter: $$7a.\,$$
7. Longer diagonal: $$P_{d}=\frac{a}{2\cdot \sin(\frac{\frac{\pi}{2}}{7})} =\frac{a}{2\cdot \sin(\frac{\pi}{14})}$$
8. Shorter diagonal: $$P_{k}=a\cdot 2\cdot \cos(\frac{\pi}{7})$$
9. Height: $$h=\frac{a}{2\cdot \tan(\frac{\frac{\pi}{2}}{7})} =\frac{a}{2\cdot \tan(\frac{\pi}{14})}$$
10. Number of diagonals of a regular heptagon: 14

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