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## GBK Geometry

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**GBK Geometry**Jordan Johnson**Today’s plan**• Greeting • Review Asg #85: • From Ch. 13, Lesson 1 (pp. 530-535): • Exercises 1-14, 46-48. • From Ch. 13, Lesson 2 (pp. 537-539): • Easy: 1-2, 6-12. Med: 29-31. • Bonus: Set III from Ch. 13, Lesson 1. • Lesson: Regular Polygons – Conclusion • Homework / Questions • Clean-up**Regular Polygon Perimeter & Area**or 6r (or we could write r⁄2 instead) or 3⁄2 or (33⁄2)r2**A 10,000-gon**• n = 10,000 ☺ • Central radius/apothem angle = 180°⁄10,000 • Side length = 2r sin(180°⁄10,000) • Apothem = r cos(180°⁄10,000) • Perimeter = 20,000r sin(180°⁄10,000) • Area = 10,000r2 sin(180°⁄10,000)cos(180°⁄10,000)**How about an**n-gon?**10,000-gon n-gon**• Central radius/apothem angle = 180°⁄10000 = 180°⁄n • Side length = 2r sin(180°⁄10000) = 2r sin(180°⁄n) • Apothem = r cos(180°⁄10000) = r cos(180°⁄n) • Perimeter = 20,000r sin(180°⁄10000) = 2nr sin(180°⁄n) • Area = 10000r2 sin(180°⁄10000)cos(180°⁄10000) = nr2 sin(180°⁄n)cos(180°⁄n)**Perimeter = 2nr sin(180°⁄n)**Area = nr2 sin(180°⁄n)cos(180°⁄n) What happens to all thisas n gets reallybig?**Perimeter = 2nr sin(180°⁄n)**Area = nr2 sin(180°⁄n)cos(180°⁄n) What happens to all thisas n gets reallybig? Let’s isolate the parts with n…**Perimeter = 2nr sin(180°⁄n)**= 2(n sin(180°⁄n))r Area = nr2 sin(180°⁄n) cos(180°⁄n) = (n sin(180°⁄n) cos(180°⁄n))r2**Perimeter = 2nr sin(180°⁄n)**= 2(n sin(180°⁄n))r Area = nr2 sin(180°⁄n) cos(180°⁄n) = (n sin(180°⁄n) cos(180°⁄n))r2**As N gets large…**• n sin(180°⁄n) approaches… • n sin(180°⁄n) cos(180°⁄n) approaches… **Perimeter = 2(n sin(180°⁄n))r** 2r Area = (n sin(180°⁄n) cos(180°⁄n))r2 r2**Full Circle**For a given radius r… The area of a circle is the limit thatthe area of an n-sided polygonapproaches as n grows. The circumference is the limit thatthe perimeter of an n-sided polygon approaches as n grows.**Homework**• Final review – due the day of the final. • Make a note card for the final. • Journal Entry #16: • What is one helpful thing you learned in geometry class about math this year? • What is one helpful thing you learned in geometry class that wasn't about math this year? • If you could change one thing about the class, what would it be? • If you could have done one thing differently, what would it be? • What advice would you give to another student who is going to take this class? • Due the end of finals week.**Clean-up / Reminders**• Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!