Regular pentagon (a two-dimensional figure) is a polygon with five 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 72°.
- Interior angles are 108°.
- 3 triangles created from any one vertex.
- Diagonals do not cross the center point of the pentagon.
- 5 diagonals
- 5 edges
- 5 vertexs
Area of a Regular Pentagon formula |
||
| \( A_{area} \;=\; \dfrac{ a\cdot r}{2} \) | ||
| Symbol | English | Metric |
| \(\large{ A_{area} }\) = area | \( in^2 \) | \( mm^2 \) |
| \(\large{ a }\) = edge | \( in \) | \( mm \) |
| \(\large{ r }\) = inside radius | \( in \) | \( mm \) |
Circumcircle Radius of a Regular Pentagon formula |
||
| \( R \;=\; \dfrac{a}{2} \cdot csc \left( \dfrac{180°}{n} \right) \) | ||
| Symbol | English | Metric |
| \(\large{ R }\) = outside radius | \( in \) | \( mm \) |
| \(\large{ a }\) = edge | \( in \) | \( mm \) |
| \(\large{ n }\) = number of edges | \( dimensionless \) | \( dimensionless \) |
Diagonal of a Regular Pentagon formula |
||
| \( D' \;=\; \dfrac{ 1 + \sqrt{ 5} }{2} \cdot a \) | ||
| Symbol | English | Metric |
| \(\large{ D' }\) = diagonal | \( in \) | \( mm \) |
| \(\large{ a }\) = edge | \( in \) | \( mm \) |
Edge of a Regular Pentagon formulas |
||
|
\( a \;=\; 25^{3/4} \cdot \dfrac{ \sqrt{ A_{area}} }{ 5\cdot \left( \sqrt{20} + 5 \right) ^{1/4 } } \) \( a \;=\; D' \cdot \dfrac { -1 + \sqrt{ 5} }{2} \) |
||
| Symbol | English | Metric |
| \(\large{ a }\) = edge | \( in \) | \( mm \) |
| \(\large{ A_{area} }\) = area | \( in^2 \) | \( mm^2 \) |
| \(\large{ D' }\) = diagonal | \( in \) | \( mm \) |
Inscribed Circle Radius of a Regular Pentagon formula |
||
| \( r \;=\; \dfrac{a}{2} \cdot cot \left( \dfrac{180°}{n} \right) \) | ||
| Symbol | English | Metric |
| \(\large{ R }\) = outside radius | \( in \) | \( mm \) |
| \(\large{ a }\) = edge | \( in \) | \( mm \) |
| \(\large{ n }\) = number of edges | \( dimensionless \) | \( dimensionless \) |
Perimeter of a Regular Pentagon formula |
||
| \( p \;=\; 5 \cdot a \) | ||
| Symbol | English | Metric |
| \(\large{ p }\) = perimeter | \( in \) | \( mm \) |
| \(\large{ a }\) = edge | \( in \) | \( mm \) |
