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Practical Uses Of Algebra

b. Practical Uses Of Algebra . B y E mma K ious. My task: is to investigate the patterns that occur within area and perimeter when enlarging various polygons. I chose the following shapes: Square, Circle. Introduction.

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Practical Uses Of Algebra

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  1. b Practical Uses Of Algebra By Emma Kious

  2. My task: is to investigate the patterns that occur within area and perimeter when enlarging various polygons. • I chose the following shapes: Square, Circle Introduction

  3. Area when shape is lengthened by 1,2,3,4,5 units for radius only.Relationship between circumference and area. What is the relationship between area of the original shape and area of the newly enlarged shape? • Area when the shape is lengthened by 1, 2, 3, 4, 5 units for the length and the width. • What is the relationship between perimeter and area and also what is the relationship between the area of the original shape and the area of the newly enlarged shape? • Predict next shape in the sequence. • Predict20thshape in the series. • Also draw comparisons between each shape you chose to focus on. E.g between the relationships you noticed when enlarging a rectangle and enlarging a triangle. Specific Instructions; investigate when:

  4. B A 1 2 1 D C 2 3 4 Squares 3 4

  5. Squares Data

  6. Area: 2, 4, 9, 16, 25, 36 • Perimeter: 4, 8, 12, 16, 20, 24 Square Numbers +4 +4 +4 +4 +4 2 4 9 16 25 36 4 8 12 16 20 24 +2 +3 +4 +0 -5 -6 Patterns

  7. Rule for area: LxW = LW Rule for perimeter: L+W+L+W = 2(W+L) Rules

  8. 1 2 4 3 Circles

  9. Circles Data

  10. Area: 3, 12, 28, 50, 78, 113 • Circumference: 6(.28),12(.56), 18(.84), 25(.12), 31(.14), 37(.42) +6.28 +6.28 +6.28 +6.28 +6.28 Patterns (rounded)

  11. Area: ∏r² Circumference: 2r ∏ Rules

  12. For the pattern in the area of circles, I couldn’t quite figure it out. • Both area and perimeter (or circumference) of squares and circles are proportionally increased Conclusion

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