Questions and Answers
What is the central angle of a regular polygon?
An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon.
What is the center of a regular polygon?
The common center of its inscribed and circumscribed circles.
What is the radius of a regular polygon?
The distance from the center of the polygon to a vertex.
What is the apothem of a regular polygon?
Signup and view all the answers
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch side?
Signup and view all the answers
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch radius?
Signup and view all the answers
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch apothem?
Signup and view all the answers
What is the area of an equilateral triangle (regular 3-gon) with a 9-inch perimeter?
Signup and view all the answers
What is the area of an equilateral triangle (regular 3-gon) with a 3-inch radius?
Signup and view all the answers
What is the area of a regular hexagon with a 4-inch side?
Signup and view all the answers
What is the area of a regular hexagon with a 48-inch perimeter?
Signup and view all the answers
What is the area of a regular hexagon with a 2√3 apothem?
Signup and view all the answers
What is the area of a regular hexagon with a 6-inch radius?
Signup and view all the answers
What is the area of a regular octagon with apothem K and side of 10?
Signup and view all the answers
If the area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches, what is the length of a side of the regular hexagon?
Signup and view all the answers
Study Notes
Central Concepts of Regular Polygons
- Central Angle: Angle formed by drawing lines to consecutive vertices from the center.
- Center: Common point for a regular polygon's inscribed and circumscribed circles, serving as its hub.
- Radius: Length from the center of the polygon to any vertex, indicating size.
- Apothem: Perpendicular distance from the center to a side, crucial for area calculations.
Area Calculations of Regular Polygons
Equilateral Triangle (Regular 3-gon)
- 6-inch Side: Area = 9√3 square inches.
- 6-inch Radius: Area = 27√3 square inches.
- 6-inch Apothem: Area = 108√3 square inches.
- 9-inch Perimeter: Area = 9/4√3 square inches.
- 3-inch Radius: Area = 27/4√3 square inches.
Regular Hexagon
- 4-inch Side: Area = 24√3 square inches.
- 48-inch Perimeter: Area = 96√3 square inches.
- 2√3 Apothem: Area = 24√3 square inches.
- 6-inch Radius: Area = 54√3 square inches.
Regular Octagon
- Apothem K and Side of 10: Area = 40K square inches.
Relationship of Geometric Figures
- Hexagon Area vs Equilateral Triangle: The area of a hexagon equals that of an equilateral triangle with a perimeter of 36 inches; side length of the regular hexagon is 2√6.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of the terminology and concepts related to regular polygons with this flashcard quiz. Each card features key terms such as central angle, radius, and apothem, essential for understanding geometric properties. Perfect for students seeking to reinforce their geometry skills.
