Download After studying this lesson, you will be able to find the areas of regular

Accelerated Geometry
Section 11.5: Areas of Regular Polygons
Name _________________________
Date__________
After studying this lesson, you will be able to find the areas of regular polygons.
Let’s start by reviewing a few triangle problems…
1. Find the area of an equilateral triangle with sides of length 8.
2. Find the area of an isosceles triangle with legs of length 10 and a base of length 4.
Recall that in a regular polygon, all sides are ________________ and all angles are _________________.
Regular polygons can be inscribed in a circle.
In regular octagon ABCDEFGH,
 O is the center of both the octagon and the circle
 OA is a radius of both the octagon and the circle
 a radius of a regular polygon is a segment joining the
center to any vertex
 How many radii can you draw in an octagon?
 How many radii can you draw in a regular polygon?
 OM is an apothem
 an apothem of a regular polygon is a segment joining the center to the midpoint of any side
 How many apothems can you draw in an octagon?
 How many apothems can you draw in a regular polygon?
 All apothems of a regular polygon are ____________________.
 Only regular polygons have ____________________.
 If a circle is inscribed in a regular polygon, then the apothem is the _________________________.
 An apothem is the ____________________________________________ of a side.
 A radius of a regular polygon _________________ an angle of the polygon.
 If all the radii of a regular polygon are drawn, the polygon is divided into _____________________
__________________________________, the altitude of which is the ______________________.
Accelerated Geometry
Section 11.5: Areas of Regular Polygons
Name _________________________
Date__________
Now let’s think about a regular n-gon.
How many sides does an n-gon have?
If we draw in all the radii, what is formed? How many are formed?
How would you find the area of the shape just formed?
Area of a regular n-gon =
__________________ x __________________
__________________ x __________________
__________________ x __________________
3. Find the area of a regular hexagon with side length of 10 inches.
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Draw radii to each vertex.
Determine the measure of the central angle.
Draw one apothem and copy that triangle separately.
Determine the measure of the angles of the triangle.
Find the unknown segments needed to find area:
 If possible, use special triangle relationships for 30-60-90 or
45-45-90 or
 Use trigonometry
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Accelerated Geometry
Section 11.5: Areas of Regular Polygons
Name _________________________
Date__________
4. Find the area of a regular octagon with a radius of 4 inches.
5. The regular pentagon has an apothem of length 12 inches. Find the shaded area.