# How To Find The Area Of A Polygon Formula The Five Most Important Concepts In Geometry

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## The Five Most Important Concepts In Geometry

After writing an article about everyday applications of geometry and another article about real-world applications of geometric principles, my head is spinning with all that I have found. Being asked what I think are the five most important points in a lesson “gives me pause.” I spent almost my entire teaching career teaching Algebra and avoiding Geometry like a plague, because I didn’t have the appreciation for its importance that I have now. Teachers who are experts in this subject may not fully agree with my choice; but I managed to settle on just 5 and I did it considering those daily uses and real world applications. Certain ideas have been repeated over and over again, so they are clearly important in real life.

The 5 most important ideas in geometry:

(1) Measure. This idea covers a lot of space. We measure distances both large, like across a lake, and small, like the diagonal of a small square. To measure a line (horizontal line), we use the appropriate units of measurement: inches, feet, miles, meters, etc. . (Don’t worry if you don’t know what a radian is. You obviously never needed that piece of information, and you probably don’t need it now. If you need to know, email me.) We measure weight–in ounces, pounds, or grams; and we measure volume: either liquid, like liters and liters or litres, or dry with measuring cups. For each of these I have given a few common units of measurement. There are many others, but you get the idea.

(2) Polygons. Here, I am referring to shapes made of straight lines, the most complicated definition but not necessary for our purposes. Triangles, triangles, and triangles are prime examples; and for each figure there are learning properties and additional measurement elements: length of individual sides, perimeter, medians, etc. Again, these are straight line measurements but we use formulas and relationships to determine the measurements. With polygons, we can also measure the space WITHIN the drawing. This is called “area,” it is literally measured in small squares inside, although the actual measurement, again, is found by formulas and written as square inches, or ft^2 (square feet).

The study of polygons will be extended to three dimensions, so that we have length, width and height. Boxes and books are good examples of 2-dimensional rectangles given a third dimension. While the “inside” of a 2-dimensional figure is called the “area,” the inside of a 3-dimensional figure is called the volume and there are, of course, formulas for that as well.

(3) Circles. Because circles are not made of straight lines, our ability to measure the distance around an area inside is limited and requires the introduction of a new number: pi. The “perimeter” is called the circumference, and both circumference and area have formulas that involve the number pi. With circles, we can talk about radius, diameter, tangent line, and different angles.

Note: There are math students who think of a circle as being made of straight lines. If you picture each of these shapes in your mind as you read the words, you will find an important pattern. Are you ready? Now, all sides in the figure are equal, picture in your mind or draw on paper a triangle, square, pentagon, hexagon, octagon, and decagon. Notice what happens? Right! As the number of sides increases, the number looks more rounded. Therefore, some people consider a circle to be a regular (all sides equal) polygon with an infinite number of sides.

(4) Skill. This is not an isolated idea, but in each Geometry topic skills are learned to do different things. These techniques are all used in construction/landscaping and many other fields as well. There are methods that allow us in real life to force the lines to be parallel or perpendicular, to force the corners to be square, and to find the exact location of a round or round object – when folding is not an option. There is a technique for dividing length into thirds or sevenths which can be very difficult with hand measurement. All of these techniques are practical practices covered in Geometry but are rarely grasped at their full potential.

(5) Conic Sections. Imagine a pointed ice cream cone. The word “conic” means cone, and the conic section means the slices of the cone. Cutting the cone in different ways produces cuts of different shapes. Cutting straight across gives us a circle. Slicing at an angle turns a circle into an oval, or ellipse. Angled differently it produces a parabola; and if the cone is doubled, the vertical slice produces a hyperbola. Circles are covered in their own chapter and are not taught like conic sections until conic sections are taught.

The main focus is on the processing of these figures — parabolic dishes to send light rays into the sky, exaggerated dishes to receive signals from space, exaggerated curves for musical instruments such as trumpets, and parabolic reflectors around a light bulb in a lamp. There are elliptical pool tables and exercise machines.

There is another idea that I am personally considering the most important of all is the study of logic. Being able to use good reasoning skills is very important and will continue to be so as our lives become more complex and more globalized. When two people hear the same words, understand the words, but come to completely different conclusions, it is because one of the parties is ignorant of the rules of reasoning. Not to put a fine point on it, but misunderstandings can start wars! Logic must be taught in a certain way all school year, and should be a required course for all college students. There is, of course, a reason why this does not happen. In fact, our politicians, and powerful people depend on an ignorant public. They rely on this to rule. An educated society cannot be manipulated or manipulated.

Why do you think it is? talking too much about improving education, but small action?

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