10.3 Areas of Regular Polygons.notebook
April 01, 2014
10.3 Areas of Regular Polygons
Objective: To find the area of a regular Polygon
Recall: A Regular Polygon has all sides congruent and all angles congruent.
Center
Radius
Radius of a Regular Polygon: the distance from the center to the vertex.
Apothem: the perpendicular distance from the center to the side.
It is important to note that the apothem bisects the vertex angle of the isosceles triangle that is formed by the radii
Apothem
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In order to solve regular polygon problems you will need to solve for missing angles. The figure below is a regular hexagon with radii and an apothem drawn. What is the measure of each numbered angle?
1
3
2
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10.3 Areas of Regular Polygons.notebook
April 01, 2014
Your Special Right Triangles will Help you for this Section:
45­45­90
30­60­90
45
30
45
60
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Area of a Regular Polygons:
The area of a regular polygon is half the product of the apothem and the perimeter.
a
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10.3 Areas of Regular Polygons.notebook
April 01, 2014
Example:
Find the area of a regular heptagon with a 9.4 in apothem and 9‐in sides.
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2) Find the area of the regular Pentagon.
10
6.88
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10.3 Areas of Regular Polygons.notebook
April 01, 2014
Find the area of the regular hexagon below.
6
6
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The side of a regular hexagon is 16 ft. What is the area of the hexagon? Round your answer to the nearest square foot.
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4
10.3 Areas of Regular Polygons.notebook
April 01, 2014
Nancy has a gazebo shaped like a regular hexagon. Each side is 5 ft long. What is the area of the gazebo? Round to the nearest whole number.
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A square has a radius equal to 6 cm and side lengths equal to 6√2 cm. Find the area.
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5
10.3 Areas of Regular Polygons.notebook
April 01, 2014
Apr 1­9:31 AM
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