I love Gardening and Geometry!

Background
My mom plans to buy 100m of edging. She wants me to figure out which shape covers the largest amount of area for her beautiful roses!

Problem
So I thought... hmmm... using 100m of edging, which shape covers the most area? What are the dimensions? Think think think!

Hypothesis
I think the CIRCLE has the largest amount of area. Why do I think this is so? Well, it has too FEW or too MANY sides (wow, infinity).

Procedure
Because meters are way too big to work with, I use centimetres. I start with a rectangle and then use a circle.

Rectangle
This is my FAVOURITE part because I make an INTERACTIVE BOARD! I love hands-on stuff! On a piece of cardboard, I draw a grid. I mark the edges and stick thumbtacks along the perimeter. I make loops out of coloured string that are 100cm long. I loop the loops around the thumbtacks to make rectangles of different dimensions (and COLOURS!) I multiply the lengths by the widths to calculate the areas and find the largest rectangle.

Results
Of all the rectangles, the SQUARE has the largest area of 625cm2! Cool! How come? I think this is because all 4 sides are equal. The other rectangles have 1 side too long and 1 side too short. The square is perfect!

Circle
I want to learn how to find the area of a circle with a perimeter of 100cm. I discover the interesting definitions for circumference, diameter and radius.

I meet a new friend called Pi! Yummy! It's a special number for all circles. I want to learn all about it. It's what I multiply the diameter by to get the circumference. ? is about 3.14. It goes on forever without a pattern.

I also use 3 fun formulas.

1. Diameter x ? = 100cm
2. Diameter = 100cm / ? = 100cm / 3.14 = 31.83cm
3. Diameter = 2 x Radius
4. Radius = Diameter / 2 = 31.83cm / 2 = 15.92cm
5. Area = Radius x Radius x ?
6. Area = 15.92cm x 15.92cm x 3.14 = 796cm2

Conclusion
My hypothesis is right: a circle does have the maximum area for mom! HOORAY! The circle with perimeter 100cm has area 796cm2. The square with perimeter 100cm has area 625cm2. My mom is thrilled that I helped her find the answer. Now we can plant the most roses!

Further Ideas
I loved doing this math project. I am so excited to learn more about geometry while helping my mom plant beautiful flowers.

Acknowledgments
I want to thank my family and my teacher Mme. Segul for encouraging me to love math more than I already do! And thank you very much!