Welcome to Geometry!

1. Welcome to Geometry! Welcome to Geometry! (An SAT problem!  ) Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters? Sit in your assigned seat. Write down your learning target. Silently start your warm-up for today. Learning Target: I will calculate the area of ANY regular polygon!

2. You have5 minutes Sit in your assigned seat. Write down your learning target. Silently work on your warm-up. Learning Target:

3. You have 4 minutes Sit in your assigned seat. Write down your learning target. Silently work on your warm-up.

4. Sit in your assigned seat. Write down your learning target. Silently work on your warm-up. You have3 minutes

5. Sit in your assigned seat. Write down your learning target. Silently work on your warm-up. You have2 minutes

6. Sit in your assigned seat. Write down your learning target. Silently work on your warm-up. You have1 minutes

7. Time’s Up! Ready for Success! Learning Target: I will calculate the area of ANY regular polygon! 1. Pencils Down 2. Body Forward 3. Eyes on Ms. Chui 4. Mouth Closed

9. FLO meetings today:

11. Deadline to apply: March 7th, 2014

12. INTERESTED??Go to the CCC during lunch and/or after school!

13. If you’re applying to programs & need help with essays, don’t be afraid to ask! 

14. Yesterday… • Naviance Quiz on Edmodo • Please complete!! • Can’t log in to Naviance? Email Ms. Doan

15. Today’s objective… • How would I find the area of this shape??

16. Use what we have learned to come up with some ideas.

17. The method we are learning today works for ANY regular polygon

18. X out the NON polygons!

19. X out the NON polygons! X X X X X

20. Polygon definition: __________________ __________________ Closed figure with straight sides

21. X out the IRREGULAR polygons! X X X X X X

22. Regular polygon definition: __________________ __________________ All sides and all angles the same

23. Switch

24. Review: How do you find the area of a rectangle? • A = bh or A = lw

25. Parallelograms are awesome So how do you find the area? What would happen if I cut a triangle off of one end of the parallelogram and translated it to the other side? A = lw or A = bh What shape have we formed?

26. Review: How do you find the area of a triangle? • A = ½ bh or A = bh/2

27. Review: How do you find the area of a circle? • A = π r 2

28. How about a pentagon? If it is a regular pentagon, it’s easy. What if we cut the pentagon into congruent triangles? If you know the height of the triangle, you can find the area. The height of one of those triangles would be perpendicular to the base and go right to the middle of the pentagon. That’s what we call the “apothem” of the polygon 12.5 cm A = ½ (b) (h) so A = ½ (18.2) (12.5) So does the formula from the formula chart for a regular polygon make sense? A = ½ aP (A = ½ the apothem times the Perimeter) 18.2 cm The area of one of the triangles is 113.75 cm2 How many triangles are there?

30. _ 1 2 a P apothem perimeter Add up all the sides!!

31. center regular polygon midpoint perpendicular (90°) | | | | The apothem is a PERPENDICULAR BISECTOR!

32. SIDE CORNER/VERTICES | | | |

33. Radius or apothem?

34. Radius or apothem?

35. Radius or apothem?

36. Radius or apothem?

38. Now for an example problem:

39. A = ½ a P 5.1 37.5 P = 7.5 * 5 P = 37.5 A = ½ a P A = ½ * 5.1 * 37.5 A = 95.625 A = 95.63 units2

40. ≈2.31

41. Practice makes Permanent! • Finished early? • Go to mschuigeometry.weebly.com • Click on Lessons • Scroll down to Thursday • Click on Extended Practice • Read the first page

42. Your HW is on the website!