8.5 Identify and Find Parts
warm-up before 8.5:
of a Regular Polygon
Classify the polygon according to its the sides.
Number of sides
Name of polygon
3
4
5
6
7
8
Learning Target:
10
I can identify and calculate the central angle, apothem, radius and side
length of a regular polygon. (G-MG.A.1)
Regular Polygon - a polygon that is equilateral and equiangular
1. Find the measure of the central angle of a regular polygon with
the given number of sides. (round to nearest tenth if needed)
a. 12 sides
radius of a polygon
- segment from center of polygon to
a vertex
______
2.
central angle of a regular polygon
- an
∠ with vertex at center and with sides being 2 radii drawn to
consecutive vertices of the polygon
360˚
- to find the measure = what do you think?
=
n
number of sides
360˚
apothem of the polygon
- perpendicular bisector from the
center to any side of the polygon
CD
⊥
AD ≅
What would be another name for the apothem
b. 21 sides
______
Name the polygon.
Draw all the radii.
How many isosceles ∆s are drawn? ______
Find the measure of central angle. ______
Using the regular hexagon ABCDEF inscribed in ⊙G, complete the following.
3. Name a central angle. ______
4. Name a radius. ______
5. Name an apothem. ______
6. m∠AGB = ______
for the isosceles ∆?
(hint: draw the radii in picture)
**** Height of the isosceles ∆
What is true about the 2 right ∆s?
7. m∠AGH = ______
8. m∠HAG = ______
9. BH ≅______
To find the the apothem, radius and the side of the polygon, we use the
central angle, the isosceles ∆s, pythagorean theorem and trigonometry.
HELPFUL HINT: Find central ∠, draw one of the isosceles ∆s,
label its sides and the central ∠, use right ∆.
10. Find the central angle and the length of the apothem.
central ∠ = ______
apothem = ______
Assignment: Worksheet 7.3
11. Find the length of one side of the polygon and the apothem.