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