1585 words - 7 pages

Polygons

Introduction:

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

| | |

Polygon

(straight sides) | Not a Polygon

(has a curve) | Not a Polygon

(open, not closed) |

Polygon comes from Greek. Poly- means "many" and -gon means "angle".

Types of Polygons

Simple or Complex

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!

| |

Simple Polygon

(this one's a Pentagon) | Complex Polygon

(also a Pentagon) |

Concave or Convex

A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180Â°. ...view middle of the document...

8Â° |

Hexacontagon | 60 | | 174Â° |

Heptacontagon | 70 | | 174.857Â° |

Octacontagon | 80 | | 175.5Â° |

Enneacontagon | 90 | | 176Â° |

Hexagon | 100 | | 176.4Â° |

Chiliagon | 1,000 | | 179.64Â° |

Myriagon | 10,000 | | 179.964Â° |

Megaton | 1,000,000 | | ~180Â° |

Googol on | 10100 | | ~180Â° |

n-gon | n | | (n-2) Ã— 180Â° / n |

Life application:

Example 1: Given- Erin is building a pen for dogs near the barn. The planned pen is hexagon in shape with sides of 3.5 m. Find the area of the pen.

Step 1: You may recall the formula for area A of regular hexagon i.e. A = 3/2(3* s2), where s is one of the sides of hexagon.

Step 2: s is 3.5 m (given), plug in value of s in the formula.

Thus, = 3/2[3* (3.5)2] = 31.8 m2

The area of the pen is 31.8 m2 (rounded), as the final answer.

Example 2: Given- The well-known building Pentagon in Arlington has the dimensions as: each side of the building is 921 ft. in length, and the apothem is 633 ft (approx.). Calculate the approx. footage enclosed at ground level of the building.

Step 1: Perimeter (P) of the building = 5 * 921 = 4605 ft.

Step 2: Area A = 1/2 * (P) * Apothem

= 1/2 * 4606 * 633 = 1457799

The footage enclosed at ground level of the building is approx. 1457799 ft2, as the final answer.

Example 3: Given- Lisa wants new carpeting for her bedroom. The bedroom is in rectangular shape wit dimensions, 10 m by 7.5 m rectangle. If carpeting costs $3/m2, how much will it cost to lay the carpet for her bedroom? You may understand the problem that involves two parts: first to find out how much carpet is needed and second the cost of the carpet.

Step 1: Calculate the area A i.e. it equals to: (10 * 7.5) = 75 m2

Step2: The carpet required is 75 m2.

The cost of carpeting is $3/m2

Step 3: Total cost = $ (75 * 3) = $225.

The cost of carpeting is $225, as the final answer.

Example 4: Given- Rob had a 10 Ft. by 15 ft. wall painted. For a wall 2.5 times as wide, the painter charged him two and a half times as much. Is this reasonable?

Step 1: The area of the wall equals (10 x 15) Ft.

Step 2: The other wall is dimensions are 2.5 times. When the dimensions of a figure are changed, the area also changes proportionally. Thus area of the other wall is two and a half times that of the first. The painter has charged 2.5 times as much. It is reasonable.

Yes, the charges are reasonable, as the final answer.

Example 5: Given- a rectangular table is 48 in wide and 66 in long. A tablecloth hangs over the table 8 in at each edge. Calculate the area of the required table cloth.

Step 1: Area of the table able cloth hangs over 8 in on each edge.

Thus dimensions of the table cloth are: w = (48 +16) = 64 in,andl= (66 +16) = 82 in.

Step 3: Area of the table cloth equals to (82 * 64) = 5248 in2

The area of the required table cloth is 5248 in2, is the final answer.

Example 6: Given- Kelly wants to add a triangular deck in the yard behind her house. Each side is...

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