Circumference, Area, and Pie

After taking a picture of this fruit pie (because everyone takes a picture of their food before they eat it these days) I noticed that this pie was a perfect example of a circle, and using some simple formulas, I could find its circumference and area.

After measuring a radii of the circle, I was able to calculate the area and circumference using the formulas shown above. 

But, why stop there? It also became apparent that I could inscribe a polygon inside the circle, and calculate the area of that as well. In this case, I used a trapezoid.

As shown above, I was able to calculate the area of this trapezoid using Theorem 11-5.

It's seems that everything, even a fruit pie, has some relation to math, and more specifically: geometry. 

-RO5

Home Decorating

My mom wanted to buy fabric to cover our semicircle window, and she wanted to know how many feet of the fabric to buy, and how much adhesive she needed in order to put it up. In order to find the area, I used ½(3.14)(30^2), which ended up to be 1413.71 in, or about 118 ft. Consequently, I told my mom to buy around 150 ft of fabric, in order to have enough. Next, I found half of the circle's circumference, plus the diameter, which ended up in resulting in 154.25 in, or about 12.85 feet.
(~KR2)

Geometry in Action

 

My dad recently asked me what would be larger: a circle in which you increase the circumference by 2, or a circle in which you increase the radius by two. Using a few formulas (C=2πr; A=πr^2), it became apparent that the circle in which you increase the radius by two is considerably larger. I was able to illustrate this in GSP so you could get a dramatic visual of the question. (TF-2)