Name:



Name: _____________________________ Date: __________________ Hr: ______

Unit 10 WS #1 Rectangle Area & Perimeter

REVIEW:

1. Suppose each of the squares in the picture below has side length 1 cm. What would be the perimeter and the area of the figure?

Perimeter = _________________ Area = ____________

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2. In your own words, what do area and perimeter mean? How are they measured.

Perimeter:

Area:

3. Would the following things be measured using an area or a perimeter? Fill in the blank with your choice.

(a) The amount of wallpaper needed to cover a wall. _______________________

(b) The amount of base board to run around the bottom edge of the wall in this classroom. ___________

(c) The amount of fence to put around a pool. _________________

(d) The amount of paper to cover a bulletin board. __________________

(e) The amount of border to put around the outside edge of the bulletin board. ____________________

Part A: Building Rectangles with the Same Areas

1. Use the tiles provided to build all noncongruent rectangles with an area of 18 square units. Draw each rectangle you find on the grid provided, and then fill in the table with the details about each rectangle.

[pic]

|Length |Width |Area |Perimeter |

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2. Repeat the activity from #1, but this time build rectangles with an area of 24 square units.

[pic]

|Length |Width |Area |Perimeter |

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3. Repeat the activity from #1, but this time build rectangles with an area of 72 square units. (In this case, only FOUR of the rectangles that can be built fit on the graph paper. Just draw those four, but list ALL rectangles you find in the table).

[pic]

|Length |Width |Area |Perimeter |

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Study the results of questions 1-3 above, and look for patterns to answer the following questions:

4. How do the shapes of the tables with the greatest perimeter compare to those with the lowest perimeter for any particular area?

5. If you had 100 tiles to make into a rectangle, what is the greatest perimeter you could have? Fill in the details about the resulting rectangle below:

Greatest _________ Length _______ Width _______

What is the lowest perimeter you could have with 100 tables? Fill in the details:

Lowest _________ Length _______ Width _______

6. What if you had 200 tiles to make into a rectangle? What is the greatest and lowest perimeter you could have? Fill in the details about the resulting rectangles below:

Greatest _________ Length _______ Width _______

Lowest _________ Length _______ Width _______

7. What if you had 200 tiles to make into a rectangle? What is the greatest and lowest perimeter you could have? Fill in the details about the resulting rectangles below:

Greatest _________ Length _______ Width _______

Lowest _________ Length _______ Width _______

Part B: Building Rectangles with the Same Perimeters

8. Use the tiles provided to build all noncongruent rectangles with an perimeter of 12 units. Draw each rectangle you find on the grid provided, and then fill in the table with the details about each rectangle.

[pic]

|Length |Width |Area |Perimeter |

|5 | | |12 |

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9. Repeat the above activity, but this time building rectangles with a perimeter of 14 units.

[pic]

|Length |Width |Area |Perimeter |

| | | |14 |

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10. Repeat the above activity, but this time building rectangles with a perimeter of 16 units.

[pic]

|Length |Width |Area |Perimeter |

| | | |16 |

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11. Repeat the above activity, but this time building rectangles with a perimeter of 18 units.

[pic]

|Length |Width |Area |Perimeter |

| | | |18 |

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12. Repeat the above activity, but this time building rectangles with a perimeter of 20 units.

[pic]

|Length |Width |Area |Perimeter |

| | | |20 |

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13. Repeat the above activity, but this time building rectangles with a perimeter of 22 units.

[pic]

|Length |Width |Area |Perimeter |

| | | |22 |

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Study the results of questions 8-13 above, and look for patterns to answer the following questions:

14. In each case describe the kind of rectangle that has the largest area.

15. In each case describe the kind of rectangle that has the smallest area.

16. If a rectangle has length l and width w, write formulas which will find its area and perimeter:

Arectangle =

Prectangle =

17. If the perimeter of a rectangle is 28 units and the length and width are whole numbers, predict the largest and smallest areas that can be made.

Greatest _________ Length _______ Width _______

Lowest _________ Length _______ Width _______

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