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Obtaining the general equation to the area of regular polygon
Introduction
In Primary School, we learned that a regular polygon can be divided into a number of congruent, equilateral triangles. This number is the same as the polygon’s number of sides. The area of the polygon can be calculated by adding up the areas of all these triangles. We hope to investigate the relationship between a polygon’s area and its number of sides and the length of each side in the end. As a final result, we hope to come up with a formula to calculate the area of any regular polygon and do some further exploration.
Mathematical Investigation / Exploration
When we first started to consider the ways of finding the area of polygons, we inspected the characteristics of regular polygon and discovered that each regular polygon are made up of identical isosceles triangles and the number of these triangles is exactly the same as the number of sides. We also know that two identical right-angled triangles will be formed if we bisect the isosceles triangle.
By using the tangent law, we can express the adjacent side of the right-angled triangle in terms of the number of sides and the length of each side. Therefore in order to obtain the area, we just need to know the number of sides and the length of them.
We let the length of the sides be n and the number of sides be s and here we are going to obtain the general formula step by step:
The General Equation to the Area of Regu...
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...blems. In the project, we have encountered numerous difficulties. Sometimes, we need to finish it by ourselves or sometimes even seek help from teachers. These experience will surely change us and allow us to face more challenging problems in the future. This project will surely equip us to be a better communicator, a person who could think more critically and a creative person who would be able to solve a problem with different methods.
Conclusion
The area of any regular polygons can be found with the below formula and we can find the value of pi using our formula.
A =
Where: n = the number of sides s = the length of one side
A = area of regular polygon
Bibliography or References
Found at: http://formulas.tutorvista.com/math/sine-cosine-tangent-formulas.html
Found at: http://lotsasplainin.blogspot.hk/2010/02/wednesday-math-vol-108-trigonometry-and.html
BUT if we want the same perimeter (which we do) we have to take away a
After 3rd century BC, Eratosthenes calculation about Earth's circumference was used correctly in different locations such as Alexandria and syene (Aswan now) by simple geometry and the shadows cast. Eratosthenes's results undertaken in 1ST century by Posidonius, were corroborated in Alexandria and Rhodes by the comparison between remarks is excellent.
The math concept of Geometry or shapes will be taught to a second-grade classroom during and after the reading of The Greedy Triangle (1994) by Marilyn Burns. We will discuss the different shapes, their attributes, how they are used and how many sides and angles each shape has.
...e that the individual and interpersonal level do have a major impact on their decision and participation. Finally it has shown changes which could be made to improve performance within the class/individual and how the framework can help in improvement and self-realisation of problems.
= 169 And so 5² + 12² = 25 + 144 = 169 = 132 b) The Numbers 7, 24, 25 also satisfy the condition. 7² + 24² =25² Because 7² = 7x7 = 49 24² = 24x24 = 576 25² = 25x25 = 525 And so 7² + 24² = 49+ 576 = 625 = 25² Task2: The perimeter and area of the triangle are: Perimeter = 5 + 12 + 13 = 30 units Area = ½ x 5 x 12 = ½ x 60 = 30 square units a) 5 12 13 [IMAGE] b) 24 7 25 [IMAGE] Perimeter = 7 + 24 + 25 = 56 units Area = ½ x 7 x 24 = ½ x 168 = 84 square units [IMAGE] Length of shortest side Length of middle side Length of longest side Perimeter Area 3 4 5 12 6 5 12 13 30 30 7 24 25 84 84 Task3: Length of short side is going to be in fixed steps meaning that this is a linear sequence and the length of middle side and longest side is actually a quadratic sequence because they are not in fixed steps and in geometric sequence.
A cube a total of 6 sides, when it is places on a surface only 5 of
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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
The foundations of mathematics are strongly rooted in the history and way of life of the Egyptian people, dating back to the fourth millennium B.C. in Egypt. Egyptian mathematics was elementary. It was generally arrived at by trial and error as a way to obtain desired results. As such, early Egyptian mathematics were primarily arithmetic, with an emphasis on measurement, surveying, and calculation in geometry. The development of arithmetic and geometry grew out of the need to develop land and agriculture and engage in business and trade. Over time, historians have discovered records of such transactions in the form of Egyptian carvings known as hieroglyphs.
* Surface Area - This will not affect any of my results, as we are
Deep within the realm of fractal math lies a fascinating triangle filled with unique properties and intriguing patterns. This is the Sierpinski Triangle, a fractal of triangles with an area of zero and an infinitely long perimeter. There are many ways to create this triangle and many areas of study in which it appears.
...one, therefore each member of the group plays an active role in the completion of the task. Also the project must include intellectually dense divergent questions, with multiple answers, and also include questions that encourage critical thinking skills. Having the freedom to think without the constraints of coming up with a single precise answer will imbue the students with the confidence to think differently, display their creativity and work at their own pace. Hereby leading to a more comprehensive and thorough answer which would encourage longer retaining of the information. This is a positive alternative for students because instead of having to stay awake all night and cramming for exams, and then forgetting the information as soon as the test is over. The students can finally acquire knowledge they can retain forever or; at least for a longer period of time.
In geometry the three dimensions are known as length, width and height or any three perpendicular directions can act as 3D. The basic three dimensional shapes are listed below. In online students can get the help about three dimensional shapes. Students can get the formulas and example problems in online. In this article we shall see how to calculate the volume and surface area of three dimensional shapes.
There is always room in mathematics, however, for imagination, for expansion of previous concepts. In the case of Pascal’s Triangle, a two-dimensional pattern, it can be extended into a third dimension, forming a pyramid. While Pascal himself did not discover nor popularize it when he was collecting information on the Triangle in the 17th century, the new pattern is still commonly called a Pascal’s Pyramid. Meanwhile, its generalization, like the pyramid, to any number of dimensions n is called a Pascal’s Simplex.