1. Review Polygon Interior Angles Theorem
The interior angles of a polygon have
a sum of 180(n – 2)o.
Regular Polygon Interior Angles Corollary
The measure of each interior angle of a
regular polygon can be found with

2. Review Polygon Exterior Angles Theorem
The exterior angles of a polygon add to 360o.
Regular Polygon Exterior Angles Corollary
The measure of each exterior angle of a
regular polygon can be found with

3. Review Area of an Equilateral Triangle Area of a Regular Polygon
a is the apothem
(distance from the center to a side).
P is the perimeter

4. Review Regular Polygon Central Angle Trigonometric Ratios and
The measure of each central angle
in a regular polygon is
Trigonometric Ratios and
Special Right Triangle Theorems
are often used when finding the area
of regular polygons.

5. Perimeters and Areas of Similar Figures 11.3
California State Standards
4: prove theorems involving congruence
and similarity
8: Solve problems involving perimeter and area.
11: Determine how changes in dimensions affect
the perimeter, area and volume of figures.

6. Areas of Similar Polygons
theorem
Areas of Similar Polygons
If two polygons are similar with a
scale factor of a:b
then the ratio of their areas is
a2:b2

7. trapezoidI ~ trapezoidII ka I
theorem
trapezoidI ~ trapezoidII ka I kb II

8. L S example hexagonL ~ hexagonS the scale factor is 3:2
Find the ratio of the perimeters S
Find the ratio of the areas

9. $125 example A rectangular tablecloth is 60 in by 120 in.
A rectangular placemat made from the same
cloth is 12 in by 24 in. The placemat costs $5.
Compare the areas of the placemat and the
tablecloth to find a reasonable cost for the
tablecloth.
scale factor
ratio of areas
cost comparison
$125

10. 328.75 ft2 example A store sells trampolines that are all regular
hexagons. One trampoline has a side length
of about 4.5 ft. and an area of about 52.6 ft2.
Find the area of the trampoline whose
perimeter is 67.5 ft.
scale factor
ratio of areas
area comparison
ft2