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Questions and Answers
What is the central angle of a regular polygon?
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?
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?
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?
What is the apothem of a regular polygon?
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch side?
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch side?
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch radius?
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch radius?
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch apothem?
What is the area of an equilateral triangle (regular 3-gon) with a 6-inch apothem?
What is the area of an equilateral triangle (regular 3-gon) with a 9-inch perimeter?
What is the area of an equilateral triangle (regular 3-gon) with a 9-inch perimeter?
What is the area of an equilateral triangle (regular 3-gon) with a 3-inch radius?
What is the area of an equilateral triangle (regular 3-gon) with a 3-inch radius?
What is the area of a regular hexagon with a 4-inch side?
What is the area of a regular hexagon with a 4-inch side?
What is the area of a regular hexagon with a 48-inch perimeter?
What is the area of a regular hexagon with a 48-inch perimeter?
What is the area of a regular hexagon with a 2√3 apothem?
What is the area of a regular hexagon with a 2√3 apothem?
What is the area of a regular hexagon with a 6-inch radius?
What is the area of a regular hexagon with a 6-inch radius?
What is the area of a regular octagon with apothem K and side of 10?
What is the area of a regular octagon with apothem K and side of 10?
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?
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?
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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.
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