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Optimum Area and Perimeter

Optimum Area and Perimeter. Second Attempt at Lesson. 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 .

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Optimum Area and Perimeter

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  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 110m2

  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. • The maximum swimming area that can be enclosed with 220m of rope. • The minimum rope needed to enclose a 3200m2 swimming area.

  6. Example - Max Area

  7. Example – Min. Perimeter

  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 1200m2 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

  13. Pg. 433 # 11

  14. Daddy Day Care

  15. Miss N’s Garden

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