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

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

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

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.

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.

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

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

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

$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

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 328.75 ft2