Practical Uses Of Algebra

By Emma Kious

b

IntroductionMy task: is to investigate the patterns

that occur within area and perimeter when enlarging various polygons.

I chose the following shapes: Square, Circle

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. Predict20th 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.

D CBA

Squares

1

12

2

3

3

4

4

Square Length Width Perimeter Area

A 1 1 4 2

B 2 2 8 4

C 3 3 12 9

D 4 4 16 16

Prediction 5 5 20 25

Prediction 20 20 80 400

Squares Data

Area: 2, 4, 9, 16, 25, 36

Perimeter: 4, 8, 12, 16, 20, 24

Patterns

+4 +4 +4+4 +4

Square Numbers

2 4 9 16 25 36

4 8 12 16 20 24

+2 +3 +4 +0 -5 -6

Rule for area: LxW = LW

Rule for perimeter: L+W+L+W = 2(W+L)

Rules

Circles1

2

3 4

Circle Radius Circumference Area

1 6.28 3.14

2 12.56 12.56

3 18.84 28.26

4 25.12 50.14

Prediction 5 31.14 78.5

Prediction 20 125.6 1256

Prediction 100 628 31400

Circles Data

Area:

3, 12, 28, 50, 78, 113

Circumference:

6(.28), 12(.56), 18(.84), 25(.12), 31(.14), 37(.42)

Patterns (rounded)

+6.28 +6.28 +6.28 +6.28 +6.28

Rules

Area: ∏r²Circumference: 2r ∏

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