# Regular Heptagon

on . Posted in Plane Geometry

• Regular heptagon (a two-dimensional figure) is a polygon with seven congruent sides.
• Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
• Congruent is all sides having the same lengths and angles measure the same.
• Diagonal is a line from one vertices to another that is non adjacent.
• Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
• Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
• Exterior angles are 51.429°
• Interior angles are 128.571°
• 14 diagonals
• 7 edges
• 7 vertexs

## Area of a Regular Heptagon formula

$$\large{ A_{area} = \frac {7} {4} \;a^2 \; \cot \;\left( \frac {180°} {7} \right) }$$
Symbol English Metric
$$\large{ A_{area} }$$ = area  $$\large{ in^2 }$$  $$\large{ mm^2 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \cot }$$ = cotangent $$\large{ in }$$ $$\large{ mm }$$

## Edge of a Regular Heptagon formula

$$\large{ a = \frac {p}{7} }$$
Symbol English Metric
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ p }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$

## Edge of a Regular Heptagon formula

$$\large{ p= 7 \;a }$$
Symbol English Metric
$$\large{ p }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$