A pentagon is a geometric figure that is made up of 5 vertices or 5 sides regular, within geometry it is considered as a polygon. There are many ways to draw a pentagon, then we will detail each one of them.
How to make a pentagon?
The pentagons can be regular and irregular polygons, which, as we know, differ in having all their sides of the same length or not. Next, we will show you how to make a simple pentagon step by step, using only a conventional ruler.
Step #1: Start by drawing a circle✔
Draw a regular circumference of the desired diameter.
Step #2: Divide it into 5 points✔
Use the central point and with the help of a protractormeasures angles of 72°, in total there will be 5 points on the circle, because if a circumference consists of 360° between 5 vertices that the pentagon has, the result is 72°.
Step #3: Join the dots together✔
Connect the adjacent points to each other, then a regular polygon will be formed, with all its sides equal.
Step #4: It’s time to erase the circle✔
erase the circle after obtaining the desired figure.
this pattern works also to form a pentagrambut instead of joining adjacent points, they join opposite ones.
How to Make a Pentagon Inside a Circle?
To do a pentagon inscribed in a circle you will need a complete geometric game (ruler, squares and protractor) and a compass. This method will allow to obtain a perfect pentagon.
Step 1.- Start with the circumference
Draw the circumference. To do this, make a central point and open the compass to the extent you want and draw a circle from that central point.
Step 2.- draw a cross
Trace two perpendicular diameter lines using a set square and squarethere will be a cross inside the circumference (a horizontal line that would be the segment AB and a vertical line CD where they cross at the central point).
Step 3.- Draw an arc from point “B”
draw an arc with compass using the radius of the circumference as a measure, the arc starts from the horizontal right end at point B.
Step 4.- Line to generate point “E”
draw a straight line to join the points where you cut the arc the circumference. A new point E is generated on the horizontal line.
Step #5.- Generate point “F”
open compass from point E to point C on the vertical line and from that measurement draw an arc, cutting the line AB, generating a point F and touching the point D.
Step #6.- Width on one of its sides
The measurement from F to the top point C represents the width on one side of the pentagon.
Step #7.- Trace the 5 points of the pentagon
Position the compass again at C and extend it to point F. From there draw a small curve towards the line of the circumference, thus obtaining point 1. Using that measurement, we position the compass at point 1 and draw another curve down the line of the circumference to obtain point 2 and so on. , we will make small arcs around the circumference. At the end there will be 5 points left.
Step #8.- Join the 5 plotted points
The 5 points are the vertices of the pentagonso what you have to do is join each of the points in order to obtain a pentagon inside the circumference.
This is the correct procedure of making a pentagon perfect. If you are in a technical drawing problem where you are asked to make the figure given the center and a vertex, this method can also be applied.
This is because the center of the pentagon also represents the center of the outer circumference and the measure that it has from there to one of its vertices (radius) is the same for both the circle and the pentagon.
What you should do is match the vertical diameter of the first steps with the vertex they give you the problem and from there the procedure is the same.
How to Make a Pentagon with a Side of 5cm?
These exercises often appear in geometry problemswhere they ask to make a pentagon from the side, in this case, 5cm.
Step #1: Draw point AB✔
It first is to draw the segment AB, which in this case, will be 5 cm in length. This is going to represent the first side of the pentagon.
Step #2: Perpendicular at point B✔
Follow draw a perpendicular to this segment AB, but let it touch point B.
Step #3: Draw point C✔
With the help of a compass, position its center in center B and with a radius of 5cm until it reaches point Awe make a perpendicular cut curve, in order to obtain a point C.
Step #4: Draw point D✔
We apply a perpendicular bisector from the segment ABwhich will provide point D.
Step #5: Draw point E✔
We use the compass again, but this time positioning at point D and opening its radius to point C. When turning the compass it will make a cut in the prolongation of AB towards the side of Bthus obtaining point E.
Step #6: Mark the 1st vertex✔
Again We center at point A with the compass and open up to point E. Now what we do is draw an arc or half circle, until we cut the line of the perpendicular bisector made initially from AB, thus obtaining point 1, which will be a new vertex of the pentagon.
Step #7: Mark vertices 2 and 3✔
Now we put 5 centimeters of radius in our compass, We make a center at points A, B and 1, draw small cuts and points 2 and 3 will be obtained.
Step #8: Connect all the dots✔
What remains is to join the segments A, B, 1, 2 and 3. Once obtained the vertices of the pentagonor, we just have to unite them.
How to Make a Pentagon with Compass?
The compass is a excellent tool for making a pentagon. It allows to create a totally regular figure taking advantage of the formed angles. The procedure that we will explain below consists of a few simple steps.
Step 1.- pentagon length
From a midpoint, open the compass at the length you want your pentagon to be.
Step 2.- draw a circle
When you have the size you want of your pentagon, then fix the compass on a point and rotate it tracing the circumference which will be the base of the figure.
Step 3.- angle of 720
With the help of the transporter open the compass at an angle of 72°.
Step 4.- Draw a line in the middle of the circle
Draw a vertical line that divides the circumference perfectly on two sides. It has to compulsorily touch the central point.
Step #5.- Mark point 1 and 2
Go to the top point of the line. This will be your point 1 and position the center of the compass there and with that measure of 72° make a cut on the line of the circumference to the right. This will be your point 2.
Step #6.- It’s time for points 3 and 4
Go to point 2 and do the same procedureyou will get point 3. Then do it from 3 and then from 4. In the end, you will return to point 1.
Step #7.- Link the dots
These 5 resulting points will represent the vertices of the pentagonso you have to join each of the vertices with straight lines, until you form a regular pentagon.
how to make a pentagon with a Strip of Paper?
The origami is the art of building figures from paper. Making a pentagon using this method is very easy, it is even one of the easiest figures to make in origami and the steps will be presented below.
Step #1: Take a rectangular strip of paper✔
Using the desired measurements so that it is the necessary size.
Step #2: Make a knot✔
Make a knot using the top.
Step #3: Pull the ends✔
Start pulling ends of the paper
Step #4: Press the vertices to make it flat✔
Start making a kind of straight line with the strip of paper, where are you going to count 4 pointsand after point 4, the end of the strip must be tied with the beginning of it.
Step #5: Observe a small pentagon✔
With 5 regular sides on the strip of paper.
What Are the Measurements of a Pentagon?
The measures of a pentagon are variable, they can measure 3cm, 6, 7, 10 or more centimeters on each side and it is these measurements that define whether a pentagon is a regular or irregular polygon. What is static is the number of sides and vertices, since a figure to be considered a “Pentagon” must have 5 sides and 5 vertices.
- Regular pentagons: Their sides are the same lengthfor example, all its sides measure 5 centimeters.
- irregular pentagons: Can have sides of different lengthsit can have a side of 5 centimeters, one of 7 and the other 3 of 6 cm.
How many triangles are formed in a pentagon?
To know how many triangles are formed in a pentagon, you must apply a very simple technique but that allows you to know the totality of them, called the inner star.
You simply must draw a 5-pointed star or star polygon inside the polygon. You will see many internal triangles, which you can count by applying colors so as not to miss any. In the case of regular pentagons, a total of 40 different triangles are formed, some equilateral, others isosceles and even scalene.
With regarding irregular pentagons this can vary and the internal star technique is not the most recommended for counting them.
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