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11.6 Changing Dimensions

Explore the effects of changing dimensions on the perimeter and area of shapes through various investigations. Conjecture about the relationship between dimension doubling and changes in perimeter and area.

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11.6 Changing Dimensions

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  1. 11.6 Changing Dimensions

  2. Investigation • Take a piece of paper. Fold it in half twice. • Cut along the layers, cutting out four congruent rectangles. 3) Find the perimeter and area of one rectangle. 4) Place two rectangles side by side, creating a rectangle where the length was doubled. 5) Find the perimeter and area of the new rectangle. 6) Make a conjecture about how doubling one length affects the perimeter and area.

  3. More Investigating • Find the area of a right triangle with base 3 cm and hypotenuse length 5 cm. Then double the height (and only the height, keep the base 3) and compare it to the area of the first triangle. • Find the area of a rectangle with height 12 and diagonal length 13. Then multiply the base by any number other than 2 and find the area. How do the two areas compare?

  4. What about changing both dimensions, non proportionally?

  5. Changing Dimensions Non-Proportionally Summary • Changing the dimensions non-proportionally changes the perimeter on a case by case basis. • Multiplying one dimension by k and another by h, the area is multiplied by kh.

  6. Find the height using the given information. • Find the perimeter and area. • Double all the dimensions, then find the perimeter and area. Compare these to the original perimeter and area. 32 10 57

  7. Describe how the change affects the perimeter and area

  8. Describe how the change affects the perimeter and area

  9. Describe how the change affects the perimeter and area

  10. Describe how the change affects the perimeter and area

  11. Describe how the change affects the perimeter and area

  12. Describe how the change affects the perimeter and area

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