# Elements of Architecture

## Geometric Shapes in Architecture

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## Polygons

The word polygon is derived from the Greek words meaning many angles. A
*
polygon
*
is a closed plane figure formed by three or more line segments which intersect only at their endpoints. Each endpoint is common to exactly two segments.

Example: The figures below are polygons

(figure available in print form)

The following figures are not polygons.

(figure available in print form)

Segments that form a polygon are called
*
sides
*
of the polygon, and an endpoint of any side is a
*
vertex
*
of the polygon. If two sides have a common endpoint, they are said to be consecutive. The endpoints of one side are consecutive vertices. The
*
angles
*
of a polygon are the interior angles between adjacent sides. A polygon is named by placing a capital letter on each vertex, moving consecutively around the figure in either a clockwise or counterclockwise direction. If a segment Joins two non consecutive vertices, it is called a
*
diagonal
*
of the polygon.

*
Example
*
: This is polygon ABCDE.

(figure available in print form)

Sides | Vertices | Consecutive | Consecutive | Angles | Diagonals |

Sides | Vertices | ||||

AB | A | AB and BC | A and B | ABC | AC |

BC | B | BC and CD | B and C | BCD | AD |

CD | C | CD and DE | C and D | CDE | BD |

DE | D | DE and EA | D and E | DEA | BE |

EA | E | EA and AB | E and A | EAB | CE |

*convex*if each interior angle is less than a straight angle, otherwise it is concave. If all sides are equal, the polygon is

*equilateral*, and if all angles are equal it is

*equiangular*. A

*regular polygon*is both equilateral and equiangular.

*
Example
*
:
*
Convex Polygon Concave Polygon Regular Polygon
*

(figure available in print form)

Polygons are classified according to their sides.

No. of Sides | Kind of Polygon | No.of Sides | Kind of Polygon |

3 | Triangle | 7 | Heptagon |

4 | Quadrilateral | 8 | Octagon |

5 | Pentagon | 9 | Nonagon |

6 | Hexagon | 10 | Decagon |

*: For one week keep a log of all the polygons that you observe at home, on the way to school, and in school. Tell the kinds of polygons that you have seen, the places where you have seen them, and their applications in everyday living.*

Exercises:

- 1. Which of the following are polygons?
- (figure available in print form)
- 2. Using letters name the following polygons.
- (figure available in print form)
- 3. Name the sides, the angles, and the diagonals of each polygon in example 1.
- 4. Tell whether the following polygons are convex or concave.
- (figure available in print form)
- 5. Classify each of the following polygons:
- (figure available in print form)
- 6. Are the following polygons equilateral, equiangular, or regular?
- (figure available in print form)
- 7. In the following picture identify as many polygons as possible.
- (figure available in print form)
- The polygons pictured here are:
- ______________
- ______________
- ______________
- ______________
- ______________