Areas of Regular Polygons
Areas of Regular Polygons
10-3
Honor’s
On a sheet of warm up paper:
•
Write the name of your podcast group
members (don’t write your own name)
•
Rate each member from 1-10, 10 being
“very helpful”
Area Formulas
Rhombus: .5(D1)(D2)
Trapezoid: .5(h)(b1+b2)
Kite: There ain’t one, use your common
sense!
Definitions
•
Center
– the center of the circle circumscribed
about the polygon
•
radius
– a segment drawn from the center of a
polygon to a vertex
•
apothem
– a segment drawn from the center of a
polygon that is perpendicular to a side
•
central angle
– an angle formed by two radii drawn
to consecutive vertices
radius
center
apothem
Central angle
Theorem 11.6 Area of a Regular
Polygon
•
The area of a regular n-gon with side lengths
(s) is half the product of the apothem (a) and
the perimeter (P), so
A = ½ aP, or A = ½ a • ns.
NOTE: In a regular polygon, the length of each
side is the same. If this length is (s), and
there are (n) sides, then the perimeter P of
the polygon is n • s, or P = ns
The number of congruent
triangles formed will be
the same as the number of
sides of the polygon.
More . . .
•
A central angle of a regular polygon is
an angle whose vertex is the center and
whose sides contain two consecutive
vertices of the polygon. You can divide
360
° by the number of sides to find the
measure of each central angle of the
polygon.
•
360/n = central angle
Ex: Finding the area of a regular
polygon
•
A regular pentagon
with radius 1 unit.
Find the area of the
pentagon.
B
C
A
1
1
D
Solution:
•
you must find the
apothem (or if the
apothem was given,
you must find the
radius, etc)
•
You need to find
measure of central
angle.
ABC is
360
°
/5, or 72
°
.
Solution:
•
Draw the apothem.
It is an isosceles
triangle so it bisects
the angle.
•
You now have a right
triangle and can use
trig ratios to find
the missing sides
36
°
Solution
You try…..
•
Find the area of a regular polygon with
9 sides and a radius of 10
Explore the definitions, formulas, and theorems related to regular polygons, including central angles, apothems, and perimeter calculations. Learn how to find the area of a regular polygon through examples and solutions.
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Presentation Transcript
Honors On a sheet of warm up paper: Write the name of your podcast group members (don t write your own name) Rate each member from 1-10, 10 being very helpful
Area Formulas Rhombus: .5(D1)(D2) Trapezoid: .5(h)(b1+b2) Kite: There ain t one, use your common sense!
Definitions center Central angle Center the center of the circle circumscribed about the polygon radius a segment drawn from the center of a polygon to a vertex apothem a segment drawn from the center of a polygon that is perpendicular to a side central angle an angle formed by two radii drawn to consecutive vertices
Theorem 11.6 Area of a Regular Polygon The area of a regular n-gon with side lengths (s) is half the product of the apothem (a) and the perimeter (P), so The number of congruent triangles formed will be the same as the number of sides of the polygon. A = aP, or A = a ns. NOTE: In a regular polygon, the length of each side is the same. If this length is (s), and there are (n) sides, then the perimeter P of the polygon is n s, or P = ns
More . . . A central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. You can divide 360 by the number of sides to find the measure of each central angle of the polygon. 360/n = central angle
Ex: Finding the area of a regular polygon A regular pentagon with radius 1 unit. Find the area of the pentagon. C 1 B D 1 A
Solution: you must find the apothem (or if the apothem was given, you must find the radius, etc) You need to find measure of central angle. ABC is 360 /5, or 72 . B 1 C A D
Solution: Draw the apothem. It is an isosceles triangle so it bisects the angle. You now have a right triangle and can use trig ratios to find the missing sides B 36 1 C A D
Solution B 1 C A D
You try.. Find the area of a regular polygon with 9 sides and a radius of 10
