Shapes and Their Areas
The objective of this coursework is to find out which shapes have the
biggest area. The perimeter must be 1000m, and the shapes can be
regular or irregular.
First of all I will experiment with different rectangles, the
different triangles, then pentagons. Then I will experiment with more
regular shapes (or whatever type of shape has the largest area) to see
the effect on area changing the number of sides has. I predict that
the largest shape will be a regular circle, and the more sides a shape
has and the more regular it is, the larger its area. (Taking a circle
as having infinite straight sides, not one side).
After I have experimented I will try to prove everything using
algebra. I will try and develop a formula to work out the area of any
polygon.
Rectangles
When I looked at the spreadsheet of rectangle areas I could instantly
see that the more regular the shape the larger the area.
However I also noticed that if you turned the graph of for this
spreadsheet upside down you would have a y=xsquared graph, with the
250x250 value being where the y- axis would be.
This means that the area of the values on either side of the square
have a square difference from the area of the square. This is because
if you "move" some of the perimeter (d) from length to with, (i.e.
decrease one dimension and increase the other) the perimeter has not
changed, but the equation for working out the area has.
It changes from
(250)(250) =250 squared
to
(250-d)(250+d) =250 squared - d squared.
So the area difference between a rectangle and a square of the same
perimeter is the difference from one of the squares sides and one of
the rectangles sides, squared.
Because all "real" square numbers are positive, the square will always
have the larger area.
It is very likely that this rule is the same for any shape but I must
The streetlamp outside paints shapes across the wall next to my bed. I can see them in the darkness, dull orange lines that have become familiar in my many restless nights. At the heart of their canvas, they intersect to form a rectangle. A rectangle? For months I believed in this reality of form with the inborn certainty that accompanies that which is obvious. I didn’t have to think about it. Nightly, I would study the shape in a sleep haze, unconsciously harboring knowledge of its regularity. Except that it is not a rectangle.
[IMAGE] ½ (a2 + b2) times it by the ratio of its real area to a
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This shows that there is a difference of 2cm between A and B, and B
Each shape generalizes the personalities and connections of the characters, although not in depth. Atticus is shown to have a big influence on the entire community, always maintaining his maturity and dignity. Scout’s respect is shown, as well as her special understanding connection with Boo Radley. Jem’s big heart and development of maturity can be seen in his shape and the colors designated for each part. Dill’s confident appearance and true insecurity is expressed through the edges of the shape. Calpurnia is shown as a mature caretaker that leads through example, and Bob Ewell is shown as the opposite of every moral the novel is meant to express. When the shapes are put together to create a picture with meaning, the outcome would show the different types of people, not as individuals in Maycomb, but as the actual town of Maycomb, showing that, no matter how old or how young, each person in Maycomb matters.
of view. I actually tried to break that rule later; if you make a rule then you also should
"A shape is that which limits a solid; in a word, a shape is the limit of a solid."
Areas of the following shapes were investigated: square, rectangle, kite, parallelogram, equilateral triangle, scalene triangle, isosceles triangle, right-angled triangle, rhombus, pentagon, hexagon, heptagon and octagon. Results The results of the analysis are shown in Table 1 and Fig 1. Table 1 showing the areas for the different shapes formed by using the
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Then in Euclid II, 7, it goes farther to explain that “if a straight line be cut at random, the square on the whole and that on one of the segments both together, are equal to twice the rectangle contained by the whole and said segm...
- Suface Area: if you are to change the surface area it is going to
* Surface Area - This will not affect any of my results, as we are
On the other hand, the areas that have more rounded
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