Transcription
[Music]
Now, let's draw, let's learn to draw regular polygons because they are not as easy to draw as they seem. For this, we will need a ruler, a compass, and a protractor. You should already be proficient in drawing, measuring angles, and performing single-digit divisions, which I believe you are capable of doing. So, the first polygon we will draw will be a triangle. Start with a line of 7 centimeters in the middle of the square. Then, with the compass, we will make that opening 7 centimeters and place it on one of the vertices. Now, place the sharp point of the compass on the other vertex. As you have noticed, the two curves we have drawn here have intersected and generated the third vertex. Let's name it. [Music] Joined A with C. [Music]
Well, it has turned out this way. I have already drawn the other two sides of the triangle with a ruler, and what we are going to do now is calculate the perimeter. So, the perimeter is calculated by taking the number of sides this figure has. We already know that a triangle has three sides, and we multiply it by the length of the side, which we know is 7 centimeters. We know that 3 times 7 is 21. That would be the perimeter of this triangle. [Music]
Well, the next regular polygon we are going to draw is the pentagon. We should have done the square next, but since we already did one, we will do the pentagon. If you remember, a pentagon is a figure that has five sides. We will start with a line of 5 centimeters. We will place the sharp point of the compass on the inner right vertex and leave an opening of 5 centimeters, and we will draw a curve. The next step to find the next vertex, each of the vertices, we need to know that when we draw a circumference, we are making a 360-degree turn. We will divide this turn by the number of sides the figure has. In this case, five. We will do a division: 360 divided by 5. The closest is 7. 7 times 5 is 35, which leaves 1 for 36. To make that a 10, 5 times 2 is 10. So, in the division, this means that to find the next vertex of this pentagon, we must draw an angle of 72 degrees. I place the origin of my protractor right in the center, and remember that I start the numbering from 0. 0, 10, 20, 30, 40, 90, 170. And for 72, I take two small marks, and what interests me is the intersection point on the circumference.
Well, so we already have two vertices of this pentagon, vertex A and the one we just generated, which must lie on the circumference. It cannot be outside, but on the circumference. Let's call it E. And we join them. Done. It has turned out like this. I already have the first side of my pentagon, side AB. How do I get the other sides? With the help of the compass, I place the sharp point on B and make an opening that reaches A. [Music] Without losing this opening, I will make a cut on the circumference, and there I have found the next vertex, vertex C. Without losing the opening, mind you, do not lose this opening. I place it on C and with it, I get the next vertex, vertex D. Without losing the opening, oh, it is very important that you do not lose this opening. I move it to D to find the last vertex, E. The distance between A and E must be the same. Look, it is the same here, which means the procedure was done correctly.
Now, the next step is to join, to join the successive vertices to give shape to the pentagon. Well, it should have turned out like this. Now, the next thing we are going to do is calculate the perimeter, that is, the length of its entire border, and for that, we will obviously use the ruler. We look at side AB. It is 5 centimeters, but it is not quite 6. It is one small mark before 6, meaning it measures 5.9 centimeters, or 5 centimeters and 9 millimeters. If we were to measure all the other sides, they should give us the same measurement. If each is 5 centimeters and there are nine small marks, 1, 2, 3, 4, 5, 6, 7, 8, and 9, it measures 5 centimeters and 9 millimeters. 5.9. And if we do this with all the others, we will realize that they measure the same because we have obtained a regular polygon where all its sides measure the same. So, to give the perimeter of a regular polygon, we take the number of sides. We already know that a pentagon has five sides, and we multiply it by the measure of the side, which in this case is 5.9. How is this multiplied? It is not that difficult. We place the number with the decimal point above: 5.9. Below, we place the 5. We multiply 5 by 9, which is 45, and carry 4. 5 times 5 is 25, plus 4 is 29. Since there is only one digit after the decimal point in one of these two factors, there is only one digit after the decimal point in the result. So, 29.5 centimeters, or 29 centimeters and 5 millimeters. That would be the perimeter of the pentagon.
Now, for a hexagon, but we also start with a line of 5 centimeters. We make an opening with the compass and draw a curve. We already know that when we draw the circumference, we have made a 360-degree turn. 360 divided by how many sides does a hexagon have? Six. So, in the table of 6, 6 times 6 is 36. 36 minus 36 is 0. So, now I will draw an angle of 60 degrees. [Music] Yes. [Music] We name it. We make an opening. We take the opening between A and B and place it on the circumference to find all the others. [Music] The last one naturally has to measure it, and we name it. [Music] And [Music] and we join them. It has turned out like this. The hexagon indeed has six sides, six vertices. So, we will find the perimeter of this hexagon, meaning the perimeter, you already know, is equal in a regular figure to the number of sides multiplied by the length of the side. [Music] 5 centimeters, but it has two extra small marks, 5 centimeters and 2, or 5.2. If we were to measure here, it should result in the same. If it does not give the same, it means it was done incorrectly. [Music] So, 6 times 5.2. How is this multiplication done? We place 5.2 above and 6 below. 6 times 2 is 12, carry 1. 6 times 5 is 30, plus 1 is 31. Since there is only one digit after the decimal point in the factors, there is one digit after the decimal point in the result. So, 31.2 centimeters would be the perimeter. [Music] Or what is the same, 31 centimeters and 2000.