1. The Following Polygons Are Given. All Of The Po ~ Lifestyle HUB

What is the area of a 15-gon with a perimeter of 90ft? s = 90/15 = 6 (length of each side) The area of any regular polygon with n sides of length s is: A = 135/tan(12) =~ 635.125 sq ftGiven information: A regular 15-gon given.Sum of all the exterior angles of a regular polygon is 360 0.. Formula used: The measure of an exterior angle of a regular polygon = 360 o n, when n = number of sides of the polygon. Calculation: We know that, sum of all the measures of a regular polygon is 360 o.. In a 15-gon, the total number of sides = 15.A fifteen sides polygon is called a pentadecagon.Le confinement continu et aujourd'hui je braque les projecteurs sur un petit dinosaure du nom de Gon. ↓ Me suivre ↓ Twitter : https://twitter.com/MMangasse D...The triangle, pentagon and 15-gon are the only regular polygons with odd sides which the Greeks could construct. If n = p 1 p 2 …p k where the p i are odd primes then n is constructible iff each p i is constructible, so a regular 21-gon can be constructed iff both the triangle and regular 7-gon can be constructed.

The measure of an exterior angle of a regular 15-gon

Kukuroo Mountain (ククルーマウンテン, Kukurū Maunten) is a dormant volcano located in Dentora Region of the Republic of Padokea. 1 Overview 2 Plot 2.1 Hunter Exam arc 2.2 Yorknew City arc 2.3 13th Hunter Chairman Election arc 3 Translations around the World 4 References It stands 3,722 meters (approximately 12,211 feet) above sea level,1 and is where the infamous Zoldyck Family livesPolygon consisting of 15 sides. Source. Florida Center for Instructional Technology Clipart ETC (Tampa, FL: University of South Florida, 2009)Calculator online for a regular polygon of three sides or more. Calculate the unknown defining areas, circumferences and angles of a regular polygon with any one known variables. Online calculators and formulas for a regular polygon and other geometry problems.Find an answer to your question "How many diagonals can be drawn from each vertex of a 15-gon? 11 18 12 8 None of these answers are correct." in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.

$The measure of an exterior angle of a regular 15-gon$

What is a 15-gon? - Answers

non-adjacent vertices, we can subdivide the 15-gon into 13 triangles. Each triangle has an angle sum of 180 degrees, so the sum of the interior angles of the 15-gon must be 13 · 180 = 2340 degrees. Since the 15-gon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of 2340That produced a 15-gon, and from that we can produce regular polygons with 30, 60, 120, etc., sides. Thus, a regular n -gon can be constructed if the only prime numbers that divide n are 2, 3, and 5, where 2 can be a repeated factor, but 3 and 5 are not repeated. But are there any others?Favorite Answer i) Since it is a regular polygon of 15 sides, measure of each side = 150/15 = 10 m ii) The angle at the center subtended by each side = 360/15 = 24°. Hence half of this angle = 12°Determine how many diagonals each of the following polygons has. a. Heptagon b. Decagon c. 15-gon d. n-gon a. A heptagon has diagonals. b. A decagon has diagonals. c. A 15-gon has diagonals. d. A n-gon has diagonals. (Type an expression using n as the variable.)They knew how to construct an equilateral triangle (3-gon), a square (4-gon), and a regular pentagon (5-gon), and of course they could double the number of sides of any polygon simply by bisecting the angles, and they could construct the 15-gon by combining a triangle and a pentagon. For over 2000 years no other constructible n-gons were known.

Jump to navigation Jump to go looking Regular pentadecagonA common pentadecagonTypeRegular polygonEdges and vertices15Schläfli symbol15Coxeter diagramSymmetry groupDihedral (D15), order 2×15Internal perspective (degrees)156°Dual polygonSelfPropertiesConvex, cyclic, equilateral, isogonal, isotoxal

In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon.

Regular pentadecagon

An ordinary pentadecagon is represented through Schläfli symbol 15.

A typical pentadecagon has inside angles of 156°, and with a facet length a, has an area given through

A=154a2cot⁡π15=1547+25+215+65a2=15a28(3+15+25+5)≃17.6424a2.\displaystyle \beginalignedA=\frac 154a^2\cot \frac \pi 15&=\frac 154\sqrt 7+2\sqrt 5+2\sqrt 15+6\sqrt 5a^2\&=\frac 15a^28\left(\sqrt 3+\sqrt 15+\sqrt 2\sqrt 5+\sqrt 5\correct)\&\simeq 17.6424\,a^2.\endaligned

Uses

A normal triangle, decagon, and pentadecagon can not utterly fill a airplane vertex.

Construction

As 15 = 3 × 5, a made from distinct Fermat primes, an ordinary pentadecagon is constructible the usage of compass and straightedge: The following buildings of standard pentadecagons with given circumcircle are similar to the representation of the proposition XVI in Book IV of Euclid's Elements.[1]

Compare the development according Euclid in this symbol: Pentadecagon

In the development for given circumcircle: FG¯=CF¯,AH¯=GM¯,|E1E6|E_1E_6 is an aspect of equilateral triangle and |E2E5|\displaystyle is an aspect of an ordinary pentagon.[2] The point H\displaystyle H divides the radius AM¯\displaystyle \overline AM in golden ratio: AH¯HM¯=AM¯AH¯=1+52=Φ≈1.618.\displaystyle \frac \overline AH\overline HM=\frac \overline AM\overline AH=\frac 1+\sqrt 52=\Phi \approx 1.618\text.

Compared with the first animation (with inexperienced lines) are in the following two pictures the two circular arcs (for angles 36° and 24°) circled 90° counterclockwise shown. They don't use the phase CG¯\displaystyle \overline CG, but moderately they use section MG¯\displaystyle \overline MG as radius AH¯\displaystyle \overline AH for the second circular arc (attitude 36°).

A compass and straightedge building for a given facet duration. The development is just about equal to that of the pentagon at a given side, then also the presentation is succeed by way of extension one facet and it generates a phase, right here FE2¯,\displaystyle \overline FE_2\text, which is divided consistent with the golden ratio:

E1E2¯E1F¯=E2F¯E1E2¯=1+52=Φ≈1.618.\displaystyle \frac \overline E_1E_2\overline E_1F=\frac \overline E_2F\overline E_1E_2=\frac 1+\sqrt 52=\Phi \approx 1.618\text.

Circumradius E2M¯=R;\displaystyle \overline E_2M=R\;;\;\; Side length E1E2¯=a;\displaystyle \overline E_1E_2=a\;;\;\; Angle DE1M=ME2D=78∘\displaystyle DE_1M=ME_2D=78^\circ

R=a⋅12⋅(5+2⋅5+3)=12⋅8+2⋅5+215+6⋅5⋅a=sin⁡(78∘)sin⁡(24∘)⋅a≈2.40486⋅a\displaystyle \beginalignedR&=a\cdot \frac 12\cdot \left(\sqrt 5+2\cdot \sqrt 5+\sqrt 3\right)=\frac 12\cdot \sqrt 8+2\cdot \sqrt 5+2\sqrt 15+6\cdot \sqrt 5\cdot a\&=\frac \sin(78^\circ )\sin(24^\circ )\cdot a\approx 2.40486\cdot a\endaligned

Construction for a given aspect durationConstruction for a given side length as animation

Symmetry

The symmetries of a typical pentadecagon as shown with colors on edges and vertices. Lines of reflections are blue. Gyrations are given as numbers in the middle. Vertices are coloured by way of their symmetry positions.

The regular pentadecagon has Dih15dihedral symmetry, order 30, represented by way of 15 lines of mirrored image. Dih15 has Three dihedral subgroups: Dih5, Dih3, and Dih1. And 4 extra cyclic symmetries: Z15, Z5, Z3, and Z1, with Zn representing π/n radian rotational symmetry.

On the pentadecagon, there are Eight distinct symmetries. John Conway labels those symmetries with a letter and order of the symmetry follows the letter.[3] He provides r30 for the full reflective symmetry, Dih15. He provides d (diagonal) with mirrored image traces through vertices, p with mirrored image traces via edges (perpendicular), and for the odd-sided pentadecagon i with replicate lines via both vertices and edges, and g for cyclic symmetry. a1 labels no symmetry.

These decrease symmetries lets in degrees of freedoms in defining irregular pentadecagons. Only the g15 subgroup has no degrees of freedom but can seen as directed edges.

Pentadecagrams

There are three common star polygons: 15/2, 15/4, 15/7, constructed from the similar 15 vertices of an ordinary pentadecagon, but hooked up through skipping every 2nd, fourth, or 7th vertex respectively.

There also are three regular megastar figures: 15/3, 15/5, 15/6, the primary being a compound of 3 pentagons, the second one a compound of five equilateral triangles, and the 3rd a compound of 3 pentagrams.

The compound determine 15/3 may also be loosely seen because the two-dimensional identical of the three-D compound of 5 tetrahedra.

Picture 15/2 15/3 or 35 15/4 15/5 or 53 15/6 or 35/2 15/7 Interior attitude 132° 108° 84° 60° 36° 12° Isogonal pentadecagons

Deeper truncations of the regular pentadecagon and pentadecagrams can produce isogonal (vertex-transitive) intermediate big name polygon paperwork with equivalent spaced vertices and two edge lengths.[4]

Vertex-transitive truncations of the pentadecagon Quasiregular Isogonal Quasiregular t15/2=30/2 t15/13=30/13 t15/7 = 30/7 t15/8=30/8 t15/11=30/22 t15/4=30/4 Petrie polygons

The regular pentadecagon is the Petrie polygon for some higher-dimensional polytopes, projected in a skew orthogonal projection:

14-simplex (14D)

References

^ .mw-parser-output cite.citationfont-style:inherit.mw-parser-output .citation qquotes:"\"""\"""'""'".mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free abackground:linear-gradient(transparent,clear),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")correct 0.1em heart/9px no-repeat.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration abackground:linear-gradient(clear,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")correct 0.1em heart/9px no-repeat.mw-parser-output .id-lock-subscription a,.mw-parser-output .quotation .cs1-lock-subscription abackground:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")appropriate 0.1em heart/9px no-repeat.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:assist.mw-parser-output .cs1-ws-icon abackground:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em heart/12px no-repeat.mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:none;padding:inherit.mw-parser-output .cs1-hidden-errorshow:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-maintdisplay:none;color:#33aa33;margin-left:0.3em.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em.mw-parser-output .quotation .mw-selflinkfont-weight:inheritDunham, William (1991). Journey thru Genius - The Great Theorems of Mathematics (PDF). Penguin. p. 65. Retrieved 2015-11-12 – by means of the University of Kentucky College of Arts & Sciences Mathematics. ^ Kepler, Johannes, translated and initiated via MAX CASPAR 1939. WELT-HARMONIK (in German). p. 44. Retrieved 2015-12-07 – by means of Google Books. Retrieved on June 5, 2017 ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278) ^ The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History, (1994), Metamorphoses of polygons, Branko Grünbaum

External links

Weisstein, Eric W. "Pentadecagon". MathWorld.vtePolygons (List)Triangles Acute Equilateral Ideal Isosceles Obtuse RightQuadrilaterals Antiparallelogram Bicentric Cyclic Equidiagonal Ex-tangential Harmonic Isosceles trapezoid Kite Lambert Orthodiagonal Parallelogram Rectangle Right kite Rhombus Saccheri Square Tangential Tangential trapezoid TrapezoidBy collection of aspects Monogon (1) Digon (2) Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6) Heptagon (7) Octagon (8) Nonagon (Enneagon, 9) Decagon (10) Hendecagon (11) Dodecagon (12) Tridecagon (13) Tetradecagon (14) Pentadecagon (15) Hexadecagon (16) Heptadecagon (17) Octadecagon (18) Enneadecagon (19) Icosagon (20) Icosidigon (22) Icositrigon (23) Icositetragon (24) Icosihexagon (26) Icosioctagon (28) Triacontagon (30) Triacontadigon (32) Triacontatetragon (34) Tetracontagon (40) Tetracontadigon (42) Tetracontaoctagon (48) Pentacontagon (50) Hexacontagon (60) Hexacontatetragon (64) Heptacontagon (70) Octacontagon (80) Enneacontagon (90) Enneacontahexagon (96) Hectogon (100) 120-gon 257-gon 360-gon Chiliagon (1000) Myriagon (10,000) 65537-gon Megagon (a million) Apeirogon (∞)Star polygons Pentagram Hexagram Heptagram Octagram Enneagram Decagram Hendecagram DodecagramClasses Concave Convex Cyclic Equiangular Equilateral Isogonal Isotoxal Pseudotriangle Regular Reinhardt Simple Skew Star-shaped Tangential Retrieved from "https://en.wikipedia.org/w/index.php?title=Pentadecagon&oldid=1020890844"