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Geometry Section 11.2 Notes NMV
Areas of Regular Polygons
Recall that a regular polygon is __a polygon that has bot equal sides and equal angles______________.
The center of a regular polygon is ___a point in the center that is equidistant from each vertices______
A radius of a regular polygon is __a segment joining the center and a vertex_________________.
An apothem of a regular polygon is __a segment from the center of the polygon perpendicular to the
opposite side of the polygon______. An apothem also ___bisects_____ the side of a regular polygon.
Draw an apothem in each of the diagrams below:
The area of any regular n-gon can be found by dividing the
regular polygon into n congruent triangles. This is done by
drawing the radii of the regular polygon.
A reg polygon = area of 1 triangle times the number of triangles
= ___n__  ___________
= ________________ = ______________
So the formula for the area of a regular polygon is A regular polygon = _______________
Section 11.2 page 2 Notes NMV
Examples: Find the (exact) area of each regular polygon.
12
12cm
8 in.
Round to the nearest 1000th.
Geometry Section 11.2 HW NMV
Problems 3 & 7 involve trigonometry. Round to the nearest 1000th.
1. The stop sign at the right is a regular octagon. Its perimeter is 80 inches and its height is 24 inches. Find
the apothem __________, radius __________ and area __________ of the stop sign.
STOP
Find the area of each of the regular polygons.
2.
3.
4
5.
4.
6cm
m
6.
12in
7. A decagon with sides of
length 26 in.
10
10 3
6cm
m