1. Optimum Area and Perimeter Second Attempt at Lesson

2. Note – All Four Sides The maximum area for a rectangular shape for a given perimeter is a square. The minimum perimeter for a rectangular shape for a given area is a square. **For any shape, the maximum area for a given perimeter would be a circle!!

3. Examples Find the dimensions and the optimal value for the following: –A rectangular shape with a 110m perimeter –A rectangular shape with an area of 110m 2

4. Notes – Only Three Sides The maximum area and minimum perimeter occur when the length (side parallel to the side without the border) is twice the width. l = 2w

5. Example The City of Ottawa wants to fence off a swimming area at Moonie’s Bay Beach. Find the optimal value given the information below. a.The maximum swimming area that can be enclosed with 220m of rope. b.The minimum rope needed to enclose a 3200m 2 swimming area.

6. Example - Max Area Perimeter (m)Width (m)Length (m)Area (m 2 ) 22052101050 102002000 201803600 301604800 401405600 501206000 601006000 551106050

7. Example – Min. Perimeter Area (m 2 )Width (m)Length (m)Perimeter (m) 320010320340 20160200 30106.7166.7 4080160 5064164 confirm3591.4161.4 4571.1161.1

8. Other Number of Sides Investigate … use a table!! Columns: –Perimeter –Length –Width –Area

9. Example Farmer Joe has 200m of fencing and he wants to create the following pens for his animals (pigs, chickens and goats). Find the maximum area he can enclose.

10. Example Farmer Joe has decided he needs to give his animals 1200m 2 of area. Find the minimum amount of fencing he needs to purchase.

11. Homework Retry … OR Do the First Time …  –The Garden Fence (from Handout) –Pg. 433 # 11 Two Problems (on this handout) –Daddy Day Care –Miss. Nieuwenhuis’ Garden

12. Garden Fence Perimeter (m)Width (m)Length (m)Area (m 2 ) 120257114 454216 552.5262.5 1045450 1537.5562.5 2030600 2522.5562.5

13. Pg. 433 # 11 Perimeter(m)Width (m)Length (m)Area (m 2 ) 3600/6.25 =576102682680 202484960 402088320 6016810080 7014810360 8012810240 6515810270 7513810350 7214410368

14. Daddy Day Care Perimeter (ft)Width (ft)Length (ft)Area (ft 2 ) 250102302300 202104200 301905700 401706800 501507500 601307800 701107700 551407700 651207800 62.51257812.50 confirm621267812 631247812

15. Miss N’s Garden Area (ft2)Width (ft)Length (ft)Perimeter (ft) 80240126 42072 81054 10854 98.953.7