Unit 13.3 - Area of Regular Polygons

Regular Polygon

A polygon that is both equilateral and equiangular.

Apothem

A segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon.

Central Angle of a Regular Polygon

An angle formed by two radii drawn to consecutive vertices.

105

Find the area of a regular decagon with a radius of 6. (Round your answer to the nearest tenth, if necessary.)

98.5

Find the area of a regular heptagon with a radius of 6. (Round your answer to the nearest tenth, if necessary.)

1039.2

Find the area of a regular hexagon with a perimeter of 120. (Round your answer to the nearest tenth, if necessary.)

509.2

Find the area of a regular hexagon with a perimeter of 84. (Round your answer to the nearest tenth, if necessary.)

93.5

Find the area of a regular hexagon with a side length of 6. (Round your answer to the nearest tenth, if necessary.)

166.3

Find the area of a regular hexagon with a side length of 8. (Round your answer to the nearest tenth, if necessary.)

41.6

Find the area of a regular hexagon with an apothem of 2√3. (Round your answer to the nearest tenth, if necessary.)

374.1

Find the area of a regular hexagon with an apothem of 6√3. (Round your answer to the nearest tenth, if necessary.)

117.7

Find the area of a regular nonagon with an apothem of 6. (Round your answer to the nearest tenth, if necessary.)

173.8

Find the area of a regular octagon with a side of 6. (Round your answer to the nearest tenth, if necessary.)

130.8

Find the area of a regular pentagon with an apothem of 6. (Round your answer to the nearest tenth, if necessary.)

150

Find the area of a regular polygon with a p = 25 and a = 12. (Round your answer to the nearest tenth, if necessary.)

272

Find the area of a regular polygon with a p = 32 a = 17. (Round your answer to the nearest tenth, if necessary.)

48

Find the area of a regular polygon with a perimeter of 12 and apothem of 8. (Round your answer to the nearest tenth, if necessary.)

27.7

Find the area of an equilateral triangle that has a side of 8. (Round your answer to the nearest tenth, if necessary.)

360/n; where n = number of sides

Measure of a Central Angle of a Regular Polygon.

Center of a Regular Polygon

The center of the inscribed circle about the polygon.

Radius of a Regular Polygon

The distance from the center to a vertex.