Presentation on theme: "Review Polygon Interior Angles Theorem"— Presentation transcript:
1Review Polygon Interior Angles Theorem The interior angles of a polygon havea sum of 180(n – 2)o.Regular Polygon Interior Angles CorollaryThe measure of each interior angle of aregular polygon can be found with
2Review Polygon Exterior Angles Theorem The exterior angles of a polygon add to 360o.Regular Polygon Exterior Angles CorollaryThe measure of each exterior angle of aregular polygon can be found with
3Review 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
4Review Regular Polygon Central Angle Trigonometric Ratios and The measure of each central anglein a regular polygon isTrigonometric Ratios andSpecial Right Triangle Theoremsare often used when finding the areaof regular polygons.
5Perimeters and Areas of Similar Figures 11.3 California State Standards4: prove theorems involving congruenceand similarity8: Solve problems involving perimeter and area.11: Determine how changes in dimensions affectthe perimeter, area and volume of figures.
6Areas of Similar Polygons theoremAreas of Similar PolygonsIf two polygons are similar with ascale factor of a:bthen the ratio of their areas isa2:b2
7trapezoidI ~ trapezoidII ka I theoremtrapezoidI ~ trapezoidIIkaIkbII
8L S example hexagonL ~ hexagonS the scale factor is 3:2 Find the ratio of the perimetersSFind the ratio of the areas
9$125 example A rectangular tablecloth is 60 in by 120 in. A rectangular placemat made from the samecloth is 12 in by 24 in. The placemat costs $5.Compare the areas of the placemat and thetablecloth to find a reasonable cost for thetablecloth.scale factorratio of areascost comparison$125
10328.75 ft2 example A store sells trampolines that are all regular hexagons. One trampoline has a side lengthof about 4.5 ft. and an area of about 52.6 ft2.Find the area of the trampoline whoseperimeter is 67.5 ft.scale factorratio of areasarea comparisonft2