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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

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

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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

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Regular Polygon Central Angle 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. Review

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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.

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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 a2:b2

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trapezoid I ~ trapezoid II ka I kb II theorem

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

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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 factorratio of areascost comparison $125

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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 ft 2. Find the area of the trampoline whose perimeter is 67.5 ft ft 2 scale factorratio of areasarea comparison

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