1. Practical Uses Of Algebra B y E mma K ious b

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

3. Specific Instructions; investigate when: 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. Predict20 th shape 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.

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

5. SquareLengthWidthPerimeterArea A1142 B2284 C33129 D4416 Prediction552025 Prediction20 80400 Squares Data

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

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

8. Circles 1 2 3 4

9. CircleRadiusCircumferenceArea 16.283.14 212.56 318.8428.26 425.1250.14 Prediction531.1478.5 Prediction20125.61256 Prediction10062831400 Circles Data

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

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

12. Conclusion 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