Optimum Area and Perimeter Second Attempt at Lesson.

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Presentation transcript:

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. **For any shape, the maximum area for a given perimeter would be a circle!!

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

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

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.

Example - Max Area Perimeter (m)Width (m)Length (m)Area (m 2 )

Example – Min. Perimeter Area (m 2 )Width (m)Length (m)Perimeter (m) confirm

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

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.

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.

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

Garden Fence Perimeter (m)Width (m)Length (m)Area (m 2 )

Pg. 433 # 11 Perimeter(m)Width (m)Length (m)Area (m 2 ) 3600/6.25 =

Daddy Day Care Perimeter (ft)Width (ft)Length (ft)Area (ft 2 ) confirm

Miss N’s Garden Area (ft2)Width (ft)Length (ft)Perimeter (ft)