Transcript Properties of Tangents

Area of Regular Polygons
• A regular polygon has all sides and all
angles congruent.
• You can circumscribe a circle about any
regular polygon. The center of the circle
is the center of the regular polygon.
• The radius of a regular polygon is the
distance from the center to a vertex.
• The apothem of a regular polygon is
the perpendicular distance from the
center to the sides.
Area of Regular Polygons
The area of a regular polygon is half the product of
the perimeter (p) and the apothem (a).
A=
1
ap
2
Example 1
Find the area of a regular
decathon with a 12.3 inch
apothem and 8 inch sides.
12.3”
A = ½ ap
p = 10(8) = 80”
A = (½) (12.3) (80) = 492 sq. in.
8”
Example 2
Find the area of a regular hexagon with 10cm sides.
The radii of a regular hexagon form
60 angles at the center. We can use
the 30-60-90 triangle to find the
apothem:
short leg = 5 cm
10 cm long keg  5 3 cm = a
p = 6(s) = 60 cm
1
2
A    5 3 60  150 3  259.8cm
 2
 