What is a word for the arcane equivalent of a monastery? Thus, 6 triangles can come together at every point because 6 60 = 360. (cont) [4 distinct ones by 2D rotation, 3 distinct ones by 3D rotation] To prove there are only 6 triangles, when drawing all the diagonals (lines going through the centre of mass) of a regular hexagon, I am not quite sure how to proceed. 3! let me set of this numbers, where in every number corresponds with a number of sides of every polygon.. ( 3,4,5,6,7,8,9,10 ),,let me answer how many diagonal can be drawn from the fixed vertex?? Feel free to play around with different shapes and calculators to see what other tricks you can come up with. An octagon has 20 diagonals in all. The cookie is used to store the user consent for the cookies in the category "Analytics". What do a triangle and a hexagon have in common? For the sides, any value is accepted as long as they are all the same. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Depending upon the sides and angles, an octagon is classified into the following categories: The octagon that has eight equal sides and eight equal angles is known as a regular octagon. How many angles are on a square-based pyramid? We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Answer: A total of 20 triangles can be formed. This value remains the same for all polygons, which means that the sum of exterior angles for all polygons is 360. In a regular octagon, by joining one vertex to the remaining non-adjacent vertices, 6 triangles can be formed. Starting at a random point and then making the next mark using the previous one as the anchor point, draw a circle with the compass. One triangle is formed by selecting a group of 3 vertices from the given 6 vertices. of sides)}=\color{blue}{(n-4)n}$$, $$=\color{}{\frac{n(n-1)(n-2)}{6}-n^2+3n}$$, $$N_0=\color{red}{\frac{n(n-4)(n-5)}{6}}$$. YouTube, Instagram Live, & Chats This Week! How many lines of symmetry does a scalene triangle have? Also, the two sides that are on the right and left of $AB$ are not to be picked, for else the triangle would share two sides with the polygon. The sum of an octagon's interior angles is 1080, and the sum of the exterior angles of an octagon is 360. copyright 2003-2023 Homework.Study.com. Therefore, there are 20 diagonals in an octagon. The answer is 3/4, that is, approximately, 0.433. 9514 1404 393. a pattern of two-dimensional shapes that can be folded to make a model of a solid figure prism a three-dimensional solid with two parallel identical polygon bases and all other faces that are rectangles pyramid a three-dimensional figure with a polygon base and triangle faces that meet at the top vertex a point where two sides of a polygon meet The inradius is the radius of the biggest circle contained entirely within the hexagon. rev2023.3.3.43278. The total number of hexagon diagonals is equal to 9 three of these are long diagonals that cross the central point, and the other six are the so-called "height" of the hexagon. Irregular Polygon case For convex , irregular polygons , dividing it into triangles can help if you trying to find its area. The name 'octagon' is derived from the Greek word 'oktgnon' which means eight angles. How many triangles can be formed by joining the vertices of a hexagon ? The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. The perimeter of an octagon is expressed in linear units like inches, cm, and so on. A pentacle is a figure made up of five straight lines forming a star. satisfaction rating 4.7/5. , Wie sagen Sie, bitte sehen Sie sich diese Angelegenheit an? High School Math : How to find the area of a hexagon 1.Write down the formula for finding the area of a hexagon if you know the side length. But the DIAGONAL too is made from 3 points : 2vertices and 1 centre.. And here we make a line and not a triangle.. Consider a regular polygon with $n$ number of vertices $\mathrm{A_1, \ A_2,\ A_3, \ A_3, \ldots , A_{n-1}}$ & $\mathrm{A_{n}}$, Total number of triangles formed by joining the vertices of n-sided regular polygon $$N=\text{number of ways of selecting 3 vertices out of n}=\color{}{\binom{n}{3}}$$ $$N=\color{red}{\frac{n(n-1)(n-2)}{6}}$$ Here we are choosing triangles with two sides common to the polygon. So, yes, this problem needs a lot more clarification. You can use math to determine all sorts of things, like how much money you'll need to save for a rainy day. How many triangles can be made with 13 toothpicks? How many diagonals are in a 100-sided shape? It solves everything I put in, efficiently, quickly, and hassle free. Their length is equal to d = 3 a. There is a space between all of the triangles, so theres 3 on the left and 3 on Enhance your educational performance Fill order form . Every polygon is either convex or concave. How many triangles can be formed by joining the vertices of Heptagonal? a. How are probability distributions determined? Regular octagons are always convex octagons, while irregular octagons can either be concave or convex. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. A regular octagon is an example of a convex octagon. You could also combine two adjacent triangles to construct a total of 3 different rhombuses and calculate the area of each separately. How many diagonals are in a pentagon, an octagon, and a decagon? For the regular hexagon, these triangles are equilateral triangles. Most people on Quora agreed that the answer is 24, with each row containing six triangles. The sum of the interior angles of an octagon is 1080 and the sum of its exterior angles is 360. When all else fails, make sure you have a clear understanding of the definitions and do some small examples. 5 How many triangles can be formed by joining the vertices of a regular octagon such that at least one side of the triangle is same as the side of the octagon? using the hexagon definition. How about an isosceles triangle which is not equilateral? Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Jamila has 5 sticks of lengths 2,4,6,8, and 10 inches. An equilateral triangle and a regular hexagon have equal perimeters. for 1 side we get (n-4) triangles $\implies$ n (n-4) triangles for n sides. How many intersections does an n-sided polygon's diagonal have if no 3 diagonals intersect. The interior angles are greater than 180, that is, at least one angle is a reflex angle. of the sides such that $ \ \ \color{blue}{n\geq 6}$. If the shape is closed, made up of straight lines, and has eight sides, we call it an octagon. For the regular triangle, all sides are of the same length, which is the length of the side of the hexagon they form. Joining each vertex with its opposite, the regular hexagon is divided into six equilateral triangles. The angles of an arbitrary hexagon can have any value, but they all must sum up to 720 (you can easily convert them to other units using our angle conversion calculator). The angle bisectors create two half angles which measure 60: mOAB=mOBA=60. We can do this by $nC1$ ways . How many lines of symmetry does an equilateral triangle have? How many triangles can be created by connecting the vertices of an octagon? Can't believe its free would even be willing to pay for a pro version of this app. A truncated hexagon, t{6}, is a dodecagon, {12}, alternating two types (colors) of edges. Welcome to the hexagon calculator, a handy tool when dealing with any regular hexagon. What is a hexagon? In a regular hexagon, four triangles can be created using diagonals of the hexagon from a common vertex. of triangles corresponding to one side)}\text{(No. Must the vertices of the triangles coincide with vertices of the hexagon? In a regular hexagon, four triangles can be created using diagonals of the hexagon from a common vertex. Therefore, the formula that is used to find its perimeter is, Perimeter of an octagon = Sum of all its sides, Perimeter of a regular octagon = 8a (Where 'a' is the length of one side of the octagon). Therefore, the formula to find the area of 357+ PhD Experts 4.5/5 Quality score 49073 Clients Get Homework Help Since a regular hexagon is comprised of six equilateral triangles, the How many triangles can be formed from $9$ points which some are collinear, Number of isoceles triangles formed by the vertices of a polygon that are not equilateral, Number of right triangles formed by the diagonals of an $n$-sided regular polygon, Follow Up: struct sockaddr storage initialization by network format-string. Then, after calculating the area of all the triangles, we add their areas to get the area of the octagon. Here are a few properties of an octagon that can help to identify it easily. Below is the implementation of the above approach: C++ #include <iostream> using namespace std; int No_of_Triangle (int N, int K) { if (N < K) return -1; else { int Tri_up = 0; Tri_up = ( (N - K + 1) This is very helpful, not only does it solves mathematical problems for you but it teaches you also. How many triangles exist in the diagonals intersections of an heptagon? 1.) Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. The area of an octagon is the total space occupied by it. The sum of the interior angles of an octagon can be calculated using the formula, Sum of interior angles of a polygon = (n - 2) 180, where 'n' represents the number of sides in the polygon. :/), We've added a "Necessary cookies only" option to the cookie consent popup. Six equilateral triangles are connected to create a regular Six equilateral triangles are connected to create a regular hexagon. The formula to calculate the area of a regular hexagon with side length s: (3 3 s^2)/2. How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm? A regular hexagon is composed of 12 congruent { 30^o,60^o,90^o } triangles. There are $n-4$ options to form triangle with one side common with polygon therefore the number of triangles with one side common with regular polygon having $n$ number of sides $$=n(n-4)$$ We are, of course, talking of our almighty hexagon. For a full description of the importance and advantages of regular hexagons, we recommend watching this video. The cookie is used to store the user consent for the cookies in the category "Other. Createyouraccount. =20 A quadrilateral is a closed shape with four vertices and four sides and an octagon has 8 sides and 8 vertices. = 20 So, 20 triangles are possible inside a hexagon. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. The cookie is used to store the user consent for the cookies in the category "Performance". THE SUM OF THE INTERIOR ANGLES OF A TRIANGLE IS 180. Minimising the environmental effects of my dyson brain. To arrive at this result, you can use the formula that links the area and side of a regular hexagon. quadrilateral = 4 sides, 2 diagonal formed, 8 triangles formed 3.) One C. Two D. Three. :)) Share Cite Follow answered Mar 6, 2013 at 19:45 user65382 1 Add a comment 0 Therefore, number of triangles = 6 C 3= 3!3!6! None B. Log in, WhatsApp Guess the Toothpaste brand names puzzle, Guess Marwadi Names from whatsapp emoticons. Can a hexagon be divided into 4 triangles? If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? 3! If you divide a regular hexagon (side length s) into six equilateral triangles (also of side length s), then the apothem is the altitude, and bisector. 2. This cookie is set by GDPR Cookie Consent plugin. Step-by-step explanation: For the first vertex of the triangle, there are 8 choice possibilities, for the second vertex, there are 7 possibilities and for the third vertex, there are 6 choice possibilities. ABC, ACD and ADE. How many triangles can be formed with the vertices of a pentagon? I can see 35 in a pentagon, by organising my triangles by the quantity of shapes each is constructed of: 10 triangles made of 1 shape. How many sides does a polygon have with an interior angle of 157.5 degrees? [We are choosing the vertex common to the two common sides,which can be done in $nC1$ ways. How many acute angles are in a right triangle? This fact proves to be of the utmost importance when we talk about the popularity of the hexagon shape in nature. Great learning in high school using simple cues. What is the point of Thrower's Bandolier. Proof by simple enumeration? Similarly, there are $(n-4)$ different triangles with only one side $A_2A_3$ common & so on. I have no idea where I should start to think. They completely fill the entire surface they span, so there aren't any holes in between them. The perimeter of an octagon is the total length of its boundary. How many triangles can be drawn in a heptagon? How many degrees is the sum of the measures of the interior angles of a regular polygon with 18 sides? Number of triangles contained in a hexagon = 6 - 2 = 4. How many different triangles can be formed with the vertices of an octagon? How many equilateral triangles in the plane have two vertices in the set {(0,0),(0,1),(1,0),(1,1)}? Sides of a regular hexagon are equal in length and opposite sides are parallel. Since the interior angles of each triangle totals. ): Drawing all 9 diagonals of a regular hexagon divides it into 24 regions, of which 6 are quadrilaterals, leaving 18 triangles. Since a regular hexagon is comprised of six equilateral triangles, the. . . On top of that, the regular 6-sided shape has the smallest perimeter for the biggest area among these surface-filling polygons, which makes it very efficient. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? Alternatively, one can also think about the apothem as the distance between the center, and any side of the hexagon since the Euclidean distance is defined using a perpendicular line. In the adjoining figure of a pentagon ABCDE, on joining AC and AD, the given pentagon is divided into three triangles i.e. This is a significant advantage that hexagons have. As shown in attachment if we a diagonals from one vertex then only 3 diagonals are drawn which results into 4 triangles. The formula for the area of a polygon is always the same no matter how many sides it has as long as it is a regular polygon: Just as a reminder, the apothem is the distance between the midpoint of any side and the center. You will end up with 6 marks, and if you join them with the straight lines, you will have yourself a regular hexagon. Making such a big mirror improves the angular resolution of the telescope, as well as the magnification factor due to the geometrical properties of a "Cassegrain telescope". Pentagon = 5 sides, 5 diagonal formed, 40 triangles formed 4.) of sides)}=\color{blue}{(n-4)n}$$, Now, join the alternate vertices $A_1$ & $A_3$ by a straight (blue) line to get a triangle $A_1A_2A_3$ with two sides $A_1A_2$ & $A_2A_3$ common. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. This same approach can be taken in an irregular hexagon.In a regular hexagonregular hexagonFor a regular n-gon, the sum . Since a regular hexagon is comprised of six equilateral triangles, the 4 Ways to Calculate the Area of a Hexagon. In this case, there are 8 sides in an octagon. The sides of a regular octagon are of equal length. Why are Suriname, Belize, and Guinea-Bissau classified as "Small Island Developing States"? Let's draw the angle bisectors of two adjacent interior angles, and call their point of intersection O: It is easy to see that OAB is equilateral - mBAF = mABC = 120, as interior angles of a regular hexagon. All triangles are formed by the intersection of three diagonals at three different points. a) 2 b) 3 c) 4 d) 5. To get a triangle with only one side $A_1A_2$ common (As shown in figure-1 below), Join the vertices $A_1$ & $A_2$ to any of $(n-4)$ vertices i.e. The perimeter of a polygon is the total length of its boundary. hexagon = 6 sides, 9 diagonal formed, ????????? 3. In a regular octagon, all the sides are equal in length, and all the angles are equal in measure. ( n - r)!] So, the total diagonals will be 6 (6-3)/2 = 9. How many signals does a polygon with 32 sides have? 2) no of triangles with two sides common, ], So if we subtract the part $2$ and $3$ from part $1$ we will get our desired result. In a regular octagon, all the interior angles are of equal measure and each interior angle measures 135. No, an octagon is not a quadrilateral. 3. 3! How many distinct equilateral triangles exist with a perimeter of 60? After multiplying this area by six (because we have 6 triangles), we get the hexagon area formula: A = 6 A = 6 3/4 a A = 3 3/2 a = (3/2 a) (6 a) /2 = apothem perimeter /2 Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. The number of quadrilaterals that can be formed by joining them is C n 4. We have,. In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways. The next best shape in terms of volume-to-surface area ratio also happens to be the best at balancing the inter-bubble tension that is created on the surface of the bubbles. How many obtuse angles does a square have? There are six equilateral triangles in a regular hexagon. How many edges can a triangular prism have? This is interesting, @Andre considering the type of question I guess it should be convex-regular. Multiply the choices, and you are done. This effect is called the red shift. How many diagonals does a regular hexagon have? These cookies ensure basic functionalities and security features of the website, anonymously. An equilateral triangle and a regular hexagon have equal perimeters. Using this calculator is as simple as it can possibly get with only one of the parameters needed to calculate all others and includes a built-in length conversion tool for each of them. The octagon in which at least one of its angles points inwards is a concave octagon. And there is a reason for that: the hexagon angles. In a convex 22-gon, how many. Does a barbarian benefit from the fast movement ability while wearing medium armor? In case of a regular octagon, we use the formula, Perimeter of regular octagon = 8 Side length, because all the sides are of equal length. Let us discuss in detail about the triangle types. How many equal sides does an equilateral triangle have? Puzzling Pentacle. a) 5 b) 6 c) 7 d) 8. Why the $\binom{6}{3}$ doesn't work to get 18 is obvious: you create triangles using intersection points. edit: It seems I didn't know the actual definition of a diagonal: "a line joining two nonconsecutive vertices of a polygon or polyhedron.". The perimeter of the hexagon formula is simply: Area = 1/2 x perimeter x apothem. We also use third-party cookies that help us analyze and understand how you use this website. This part of the camera is called the aperture and dictates many properties and features of the pictures produced by a camera. How to react to a students panic attack in an oral exam? Can you elaborate a bit more on how you got. Regular or not? Method 1 Drawing the Diagonals 1 Know the names of polygons. There are three paths formed by the triangles A 1 A 2 A 3, B 1 B 2 B 3, and C 1 C 2 C 3, , as shown. 1 See answer Advertisement Edufirst Quadrilateral: two (you can only trace one diagonal and it forms two triangles) Hexagon: four (you can trace thre diagonals and four triangles are formed) Octagon: six (you can trace five diagonals and six triangles are formed) Degagon: eight (you can trace seven diagonals and eight triangles are formed) The most unexpected one is the shape of very bright (point-like) objects due to the effect called diffraction grating, and it is illustrated in the picture above. One C. Two D. Three. $$=\left[\frac{n(n-1)(n-2)}{6}\right]-\left[n(n-4) + n\right]$$ Learn the hexagon definition and hexagon shape. A regular hexagon is made from equilateral triangle by cutting along the dotted lines and removing the three smaller triangles. How to calculate the angle of a quadrilateral? six You can see a similar process in the animation above. Each sprinter traverses her respective triangular path clockwise and returns to her starting point. Since the interior angles of each triangle totals 180, the hexagons interior angles will total 4(180), or 720. This cookie is set by GDPR Cookie Consent plugin. ABCPQR Then,. Using a very simple formula, you can calculate the number of diagonals in any polygon, whether it has 4 sides or 4,000 sides. You may need to first identify how many sides are present in the polygon. All rights reserved. 3! Draw a circle, and, with the same radius, start making marks along it. . The interior angles add up to 1080 and the exterior angles add up to 360. we will count the number of triangles formed by each part and by taking two or more such parts together. Answer is 6. Assume you pick a side $AB$. Round 3 Admitted Student Panel, Improve your GMAT Score in less than a month, The Cambridge MBA - Committed to Bring Change to your Career, Outlook, Network. But, each diagonal is counted twice, once from each of its ends. The length of the sides can vary even within the same hexagon, except when it comes to the regular hexagon, in which all sides must have equal length. if triangle has a perimeter of 18, what is the perimeter of hexagon? How many triangles can we form if we draw all the diagonals of a hexagon? Step-by-step explanation:There are 6 vertices of a hexagon. Fill order form. How many maximum number of isosceles triangle are possible in a regular polygon of $n$ sides? Since a regular hexagon is comprised of six equilateral triangles, the . Is there a proper earth ground point in this switch box? Get access to this video and our entire Q&A library, What is a Hexagon? A place where magic is studied and practiced? For a regular hexagon, it gives you 2 equilateral triangles, 6 isoceles (non-equilateral) ones and 12 triangles with a 90 degree angle (which can be put into 2 types by 2D rotation), so 20 in total. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The answer is 3, that is, approximately 1.73. Answer is 6. Thus, there are 20 diagonals in a regular octagon. To one side of each diagonal is a triangle, and you count of those: one to that side of the first diagonal, a second one to that side of the second diagonal, and so on. In geometry, a hexagon is a two-dimensional polygon that has six sides. How many obtuse angles does a rhombus have. In triangle TAG, angle A = 70 degrees, a = 19, g = 26 A. 2 All 4 angles inside any quadrilateral add to 360. How many obtuse angles are in a triangle? regular octagon regular hexagon regular decagon |regular dodecagon mber of triangles ed in 4 O prior angle sum is 1.800 amber of triangles O ned is 6 2. If you don't remember the formula, you can always think about the 6-sided polygon as a collection of 6 triangles. Formula : Here number of vertical parts " n" and horizontal parts "m" then possible triangles is Figure - 11: Triangle counting in Fig - 11 = 30 Solution : Here number of vertical parts " 4 and horizontal parts "3" then possible triangles is 4 x 3 x 5 /2 = 30 Figure - 12: Triangle counting in Fig - 12 = 45 So actually, it's 18 triangles, not 6, as explained by Gerry Myerson. Observe the figure given below to see the regular hexagon with 6 equilateral triangles. OA is Official Answer and Stats are available only to registered users. After multiplying this area by six (because we have 6 triangles), we get the hexagon area formula: We hope you can see how we arrive at the same hexagon area formula we mentioned before. This also explains why squares and hexagons tessellate, but other polygons like pentagons won't. A square will form corners where 4 squares meet, since 4 90 = 360. 3! An octagon has eight sides and eight angles. Here, the perimeter is given as 160 units. Challenge Level. Here, n = 8, so after substituting the value of n = 8 in this formula, we get, 1/2 n (n - 3) = 1/2 8 (8 - 3) = 20. If we put three triangles next to each other, you can see they form a trapezoid: In this case we can say, "one-sixth plus one-sixth plus one-sixth equals one-half" (remember that a trapezoid is one-half of a hexagon), or we can say "three times one-sixth equals one-half." These equations can be written: 1 6 + 1 6 + 1 6 = 1 2 and 3 x 1 6 . Check out 23 similar 2d geometry calculators , How many sides does a hexagon have? $$= \frac{n(n-1)(n-2)}{6}$$ They are constructed by joining two vertices, leaving exactly one in between them. 10 triangles made of 3 shapes. In a regular hexagon, how many diagonals and equilateral triangles are formed? A regular hexagon can be dissected into six equilateral triangles by adding a center point. i.e. Minimising the environmental effects of my dyson brain. All other trademarks and copyrights are the property of their respective owners. Thus there are $n$ pairs of alternate & consecutive vertices to get $n$ different triangles with two sides common (Above fig-2 shows $n$ st. lines of different colors to join alternate & consecutive vertices). We will directly count the number of triangles with 3, 4 and 5 endpoints (top three figures). Since triangles have angle sum 180 and quadrilaterals have angle sum 360, copies of one tile can fill out the 360 surrounding a vertex of the tessellation. What kind of hexagon? This result is because the volume of a sphere is the largest of any other object for a given surface area. In order to calculate the perimeter of an octagon, the length of all the sides should be known. If you draw all diagonals of a regular hexagon you have $3 \cdot 6 = 18$ possible triangles, but 3 of those are the same (the equilateral triangles) so we have $18 - 3 = 15$ possible triangles. The number of triangles is n-2 (above). Hence number of triangles by joining the vertices of decagon is = 10C 3= 1.2.310.9.8= 120 Was this answer helpful? Here is one interpretation (which is probably not the one intended, but who knows? points and the triangle has 3 points means a triangle need 3 vertices to be formed. Analytical cookies are used to understand how visitors interact with the website. One of the most valuable uses of hexagons in the modern era, closely related to the one we've talked about in photography, is in astronomy. How many triangles do you get from six non-parallel lines? How many unique triangles can be made where one angle measures 60 degrees and another angle is an obtuse angle? In a hexagon there are six sides. In nature, as we have mentioned, there are plenty of examples of hexagonal formations, mostly due to stress and tensions in the material. How many lines of symmetry does a triangle have? Thus, the length of each side = 160 8 = 20 units. The best answers are voted up and rise to the top, Not the answer you're looking for? 4! There are 3 diagonals, so 3 triangles counted in 35 are actually a LINE.. Total left 35-3=32. In an 11-sided polygon, total vertices are 11. The three sides of a triangle have length a, b and c . Circumradius: to find the radius of a circle circumscribed on the regular hexagon, you need to determine the distance between the central point of the hexagon (that is also the center of the circle) and any of the vertices. A fascinating example in this video is that of the soap bubbles. It will also be helpful when we explain how to find the area of a regular hexagon. About an argument in Famine, Affluence and Morality. The circumradius is the radius of the circumference that contains all the vertices of the regular hexagon. How many triangles can be formed by the vertices of a regular polygon of $n$ sides? Diagonals Triangle 3 d3= 0 Quadrilateral 4 d4=2 Pentagon 5 d5= 2+3=5 Hexagon 6 d6= 2+3+4=9. It does not store any personal data. On the circumference there were 6 and then 12 on the second one. And how many if no side of the polygon is to be a side of any triangle ? Another way to find the number of triangles that can be formed in an octagon is by using the formula, (n - 2), where n = number of sides of the polygon. How many non-congruent triangles can be formed by the vertices of a regular polygon of $n$ sides. Each exterior angle of a regular hexagon has an equal measure of 60. Observe the question carefully and find out the length of side of a regular hexagon. We need to form triangles by joining the vertices of a hexagon To form a triangle we require 3 vertices. Do new devs get fired if they can't solve a certain bug? Since the sum of internal angles in one triangle is 180, it is concluded that 6 triangles, side by side, should measure up to 6x180=1080. Similarly, all the exterior angles are of equal measure and each exterior angle measures 45. Solve word questions too In addition to solving math problems, students should also be able to answer word questions.