Properties Of Regular Pentagons
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Properties of regular pentagons Interior angle
108°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a pentagon, n=5. See Interior Angles of a Polygon
Exterior Angle
72°
To find the exterior angle of a regular pentagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180interior angle. See Exterior Angles of a Polygon
Area
1.72 S2 approx Where S is the length of a side. To find the exact area of a regular pentagon or any regular polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all pentagons Number of diagonals
5
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
3
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
540° In general 180(n–2) degrees . See Interior Angles of a Polygon
Formula for the number of diagonals As described above, the number of diagonals from a single vertex is three less the the number of vertices or sides, or (n3). There are N vertices, which gives us n(n-3) diagonals But each diagonal has two ends, so this would count each one twice. So as a final step we divide by 2, for the final formula:
where N is the number of sides (or vertices)
Properties of regular hexagons Interior angle
120°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a hexagon, n=6. See Interior Angles of a Polygon
Exterior Angle
60°
To find the exterior angle of a regular hexagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area
2.598s2 Where S is the length of a side. To find the exact area of a hexagon or any polygon, using approx various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all hexagons Number of diagonals
9
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
4
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
720° In general 180(n–2) degrees . See Interior Angles of a Polygon
Properties of regular heptagons Interior angle
128.571° Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a heptagon, n=7. See Interior Angles of a Polygon
Exterior Angle
51.429°
To find the exterior angle of a regular heptagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area
3.633s2 approx
Where S is the length of a side. To find the exact area of a heptagon or any polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all heptagons Number of diagonals
14
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
5
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
900° In general 180(n–2) degrees . See Interior Angles of a Polygon
Properties of regular octagons Interior angle
135°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For an octagon, n=8. See Interior Angles of a Polygon
Exterior Angle
45°
Area
4.828s2 Where S is the length of a side. To find the exact area of an octagon or any polygon, using approx various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
To find the exterior angle of a regular octagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Properties of all octagons Number of diagonals
20
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
6
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
1080° In general 180(n–2) degrees . See Interior Angles of a Polygon
Properties of regular nonagons Interior angle
140°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a nonagon, n=9. See Interior Angles of a Polygon
Exterior Angle
40°
To find the exterior angle of a regular decagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area
6.182s2 Where S is the length of a side. To find the exact area of a decagon or any polygon, using approx various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all nonagons Number of diagonals
27
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
7
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
1260° In general 180(n–2) degrees . See Interior Angles of a Polygon
108°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a pentagon, n=5. See Interior Angles of a Polygon
Exterior Angle
72°
To find the exterior angle of a regular pentagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180interior angle. See Exterior Angles of a Polygon
Area
1.72 S2 approx Where S is the length of a side. To find the exact area of a regular pentagon or any regular polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all pentagons Number of diagonals
5
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
3
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
540° In general 180(n–2) degrees . See Interior Angles of a Polygon
Formula for the number of diagonals As described above, the number of diagonals from a single vertex is three less the the number of vertices or sides, or (n3). There are N vertices, which gives us n(n-3) diagonals But each diagonal has two ends, so this would count each one twice. So as a final step we divide by 2, for the final formula:
where N is the number of sides (or vertices)
Properties of regular hexagons Interior angle
120°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a hexagon, n=6. See Interior Angles of a Polygon
Exterior Angle
60°
To find the exterior angle of a regular hexagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area
2.598s2 Where S is the length of a side. To find the exact area of a hexagon or any polygon, using approx various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all hexagons Number of diagonals
9
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
4
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
720° In general 180(n–2) degrees . See Interior Angles of a Polygon
Properties of regular heptagons Interior angle
128.571° Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a heptagon, n=7. See Interior Angles of a Polygon
Exterior Angle
51.429°
To find the exterior angle of a regular heptagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area
3.633s2 approx
Where S is the length of a side. To find the exact area of a heptagon or any polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all heptagons Number of diagonals
14
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
5
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
900° In general 180(n–2) degrees . See Interior Angles of a Polygon
Properties of regular octagons Interior angle
135°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For an octagon, n=8. See Interior Angles of a Polygon
Exterior Angle
45°
Area
4.828s2 Where S is the length of a side. To find the exact area of an octagon or any polygon, using approx various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
To find the exterior angle of a regular octagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Properties of all octagons Number of diagonals
20
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
6
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
1080° In general 180(n–2) degrees . See Interior Angles of a Polygon
Properties of regular nonagons Interior angle
140°
Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a nonagon, n=9. See Interior Angles of a Polygon
Exterior Angle
40°
To find the exterior angle of a regular decagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area
6.182s2 Where S is the length of a side. To find the exact area of a decagon or any polygon, using approx various methods, see Area of a Regular Polygon and Area of an Irregular Polygon
Properties of all nonagons Number of diagonals
27
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles
7
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles
1260° In general 180(n–2) degrees . See Interior Angles of a Polygon
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