# how many triangles can be formed in a hexagon

How many triangles can we form if we draw all the diagonals . points and the triangle has 3 points means a triangle need 3 vertices to be formed. In the adjoining figure of a hexagon ABCDEF, on joining AC, An equilateral hexagon can be divided into 6 equilateral triangles of side length 6. We sometimes define a regular hexagon using equilateral triangles, or triangles in which all of the sides have equal length. Can you pick flowers on the side of the road? if the area of the triangle is 2 square units, what is the area of the hexagon? There is a space between all of the triangles, so theres 3 on the left and 3 on. Can a hexagon be divided into 4 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 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 Example 1: How many triangles can be formed by joining the vertices of an octagon? How many obtuse angles can a isosceles triangle have? In a regular hexagon, four triangles can be created using diagonals of the hexagon from a common vertex. , Was ist ein Beispiel fr eine Annahme? A quadrilateral is a closed shape with four vertices and four sides and an octagon has 8 sides and 8 vertices. For example, suppose you divide the hexagon in half (from vertex to vertex). On top of that, due to relativistic effects (similar to time dilation and length contraction), their light arrives on the Earth with less energy than it was emitted. This cookie is set by GDPR Cookie Consent plugin. Octagons that have equal sides are known as regular octagons, while irregular octagons have different side lengths. It reads area = 3/4 side, so we immediately obtain the answer by plugging in side = 1. A fascinating example in this video is that of the soap bubbles. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. Helped me with my math homework and it also lets you see how it's done so you can get to the right answer yourself. 3! It only takes a minute to sign up. 4 triangles are formed. However, with a little practice and perseverance, anyone can learn to love math! That is because despite being very bright objects, they are so very far away that only a tiny fraction of their light reaches us; you can learn more about that in our luminosity calculator. How many equilateral triangles are there? Observe the question carefully and find out the length of side of a regular hexagon. Thus the final result is $nC3-nC1*(n-4)C1-nC1$. Minimising the environmental effects of my dyson brain. If you are having trouble with maths I really suggest you to get this app, used this several times, and can officially say it's a lifesaver. Sum of interior angles of a polygon = (n - 2) 180 = (8 - 2) 180 = 1080. How to show that an expression of a finite type must be one of the finitely many possible values? If the shape is closed, made up of straight lines, and has eight sides, we call it an octagon. The area of an octagon is the total space occupied by it. How many lines of symmetry does an equilateral triangle have? There are 8 interior angles and 8 respective exterior angles in an octagon. 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. Starting with human usages, the easiest (and probably least exciting) use is hexagon tiles for flooring purposes. 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. I have no idea where I should start to think. Therefore, there are 20 diagonals in an octagon. Here, the perimeter is given as 160 units. 3! $$= \text{total - (Case I + Case II)}$$ 2. How do I connect these two faces together? How many angles does a rectangular-based pyramid have? If $N_0$ is the number of triangles having no side common with that of the polygon then we have $$N=N_0+N_1+N_2$$ $$N_0=N-N_1-N_2$$ $$=\binom{n}{3}-(n-4)n-n$$ $$=\color{}{\frac{n(n-1)(n-2)}{6}-n^2+3n}$$ How many equilateral triangles in the plane have two vertices in the set {(0,0),(0,1),(1,0),(1,1)}? Also, a triangle has many properties. The best way to counteract this is to build telescopes as enormous as possible. 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. - Definition, Area & Angles. How to calculate the angle of a quadrilateral? $A_4, \ A_5,\ A_6, \ \ldots \ A_{n-1}$ to get triangles with only one side common. The answer is not from geometry it's from combinations. Therefor the interior angles of the polygon must be the sum of all the triangles' interior angles, or 180 (n-2). 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) 3. THE SUM OF THE INTERIOR ANGLES OF A TRIANGLE IS 180. In a hexagon there are six sides. 2 All 4 angles inside any quadrilateral add to 360. It is calculated with the formula, Area of a Regular Octagon = 2a2(1 + 2); where 'a' is any one side length of the octagon. An octagon can be defined as a polygon with eight sides, eight interior angles, and eight vertices. Remember, this only works for REGULAR hexagons. If all of the diagonals are drawn from a vertex of a quadrilateral, how many triangles are formed? We divide the octagon into smaller figures like triangles. How many unique triangles can be made where one angle measures 60 degrees and another angle is an obtuse angle? Therefore, the length of each side of the octagon is 20 units. If she uses 3 sticks at a time as the sides of triangles, how many triangles can she make? Here is how you calculate the two types of diagonals: Long diagonals They always cross the central point of the hexagon. Log in, WhatsApp Guess the Toothpaste brand names puzzle, Guess Marwadi Names from whatsapp emoticons. Equivalent Fractions in Hexagon Drawing a line to each vertex creates six equilateral triangles, which is six equal areas. How many exterior angles does a triangle have? How many lines of symmetry does a triangle have? Let us choose triangles with $1$ side common with the polygon. One C. Two D. Three. How many triangles can be drawn in a heptagon? On the circumference there were 6 and then 12 on the second one. For example, in a hexagon, the total sides are 6. The hexagon calculator allows you to calculate several interesting parameters of the 6-sided shape that we usually call a hexagon. The number of vertices in a triangle is 3 . 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. Become a Study.com member to unlock this answer! How many different triangles can be formed with the vertices of an octagon? for 1 side we get (n-4) triangles $\implies$ n(n-4) triangles for n sides. These restrictions mean that, for a regular hexagon, calculating the perimeter is so easy that you don't even need to use the perimeter of a polygon calculator if you know a bit of math. Very great, it helps me with my math assignments. How many triangles do you get from six non-parallel lines? How many acute angles does an equilateral triangle have? Hence number of triangles by joining the vertices of decagon is = 10C 3= 1.2.310.9.8= 120 Was this answer helpful? How many right angles does a triangle have? This same approach can be taken in an irregular hexagon. 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. How many triangles can be formed by using vertices from amongst these seven points? An alternated hexagon, h{6}, is an equilateral triangle, {3}. How many diagonals does a 20 sided polygon have? In a hexagon there are six sides. The circumradius is the radius of the circumference that contains all the vertices of the regular hexagon. But, each diagonal is counted twice, once from each of its ends. Where does this (supposedly) Gibson quote come from? For those who want to know how to do this by hand, we will explain how to find the area of a regular hexagon with and without the hexagon area formula. With our hexagon calculator, you can explore many geometrical properties and calculations, including how to find the area of a hexagon, as well as teach you how to use the calculator to simplify any analysis involving this 6-sided shape. The number of triangles that make a hexagon depends on the type of hexagon and how we Our experts can answer your tough homework and study questions. Similarly, there are $(n-4)$ different triangles with only one side $A_2A_3$ common & so on. The interior angles are greater than 180, that is, at least one angle is a reflex angle. According to the regular octagon definition, all its sides are of equal length. The perimeter of a polygon is the total length of its boundary. If you preorder a special airline meal (e.g. Easy Solution Verified by Toppr There are 6 vertices of a hexagon. The sum of all the interior angles in an octagon is always 1080. 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 $$N=\text{number of ways of selecting 3 vertices out of n}=\color{}{\binom{n}{3}}$$ $$N=\color{red}{\frac{n(n-1)(n-2)}{6}}$$ How many triangles can be created by connecting the vertices of an octagon? Answer: Therefore, the number of triangles, which can be formed by joining the vertices of a hexagon is 20. Step-by-step explanation:There are 6 vertices of a hexagon. How many angles are on a square-based pyramid? How many triangles can be formed with the given information? For the hexagon what is the sum of the exterior angles of the polygon? In a regular hexagon, four triangles can be created using diagonals of the hexagon from a common vertex. Seen with two types (colors) of edges, this form only has D 3 symmetry. We also answer the question "what is a hexagon?" In a regular octagon, by joining one vertex to the remaining non-adjacent vertices, 6 triangles can be formed. a) n - 2 b) n - 1 c) n d) n + 1. These cookies track visitors across websites and collect information to provide customized ads. Get access to this video and our entire Q&A library, What is a Hexagon? Do I need a thermal expansion tank if I already have a pressure tank? Answer with solution Again it is good to use symmetry here, we can brake this image into six small triangles each formed by one of the side of the hexagon and each of the triangle is divided in half by a line. Here is one interpretation (which is probably not the one intended, but who knows? There is more triangle to the other side of the last of those diagonals. How many right triangles can be constructed? The sum of its interior angles is 1080 and the sum of its exterior angles is 360. $$N_0=\color{red}{\frac{n(n-4)(n-5)}{6}}$$ This value remains the same for all polygons, which means that the sum of exterior angles for all polygons is 360. The way that 120 angles distribute forces (and, in turn, stress) amongst 2 of the hexagon sides makes it a very stable and mechanically efficient geometry. In a regular octagon, all the sides are equal in length, and all the angles are equal in measure. The number of quadrilaterals that can be formed by joining them is C n 4. There are 6 vertices of a hexagon. How many triangle can be draw in a hexagon by joining their vertices? We divide the octagon into smaller figures like triangles. How do I align things in the following tabular environment? In a regular hexagon, four triangles can be created using diagonals of the hexagon from a common vertex. The octagon in which one of the angles points inwards is a concave octagon. These tricks involve using other polygons such as squares, triangles and even parallelograms. Here, n = 8, so after substituting the value of n = 8 in the formula, Number of triangles that can be formed in a polygon = (n - 2), we get, (8 - 2) = 6. Octagons are classified into various types based upon their sides and angles. This website uses cookies to improve your experience while you navigate through the website. Focus on your job You can provide multiple ways to do something by listing them out, providing a step-by-step guide, or giving a few options . 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. If a polygon has 500 diagonals, how many sides does the polygon have? How many edges can a triangular prism have? For a random (irregular) hexagon, the answer is simple: draw any 6-sided shape so that it is a closed polygon, and you're done. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The site owner may have set restrictions that prevent you from accessing the site. Let's say the apothem is 73 cm. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. YouTube, Instagram Live, & Chats This Week! , What are examples of venial and mortal sins? a) 1 b) 2 c) 3 d) 4. 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 . How many triangles can be formed using 10 points located in each of the sides (but not vertices) of a square? Therefore, the area of the octagon is 120.71 square units. The word 'Octagon' is derived from the Greek word, 'oktgnon' which means eight angles. 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. Most of the entries in the NAME column of the output from lsof +D /tmp do not begin with /tmp. The interior angles add up to 1080 and the exterior angles add up to 360. We are, of course, talking of our almighty hexagon. Convex or not? How many edges does a triangular prism have? We have discussed all the parameters of the calculator, but for the sake of clarity and completeness, we will now go over them briefly: Everyone loves a good real-world application, and hexagons are definitely one of the most used polygons in the world. Learn more about Stack Overflow the company, and our products. To solve this lets break this problem into $3$ parts: Total number of triangles that can form without any restrictions$=nC3$. In geometry, a hexagon is a two-dimensional polygon that has six sides. We will directly count the number of triangles with 3, 4 and 5 endpoints (top three figures). Pentagon = 5 sides, 5 diagonal formed, 40 triangles formed 4.) How many acute angles are in a right triangle? This is because of the relationship apothem = 3 side. six Observe the figure given below to see what an octagon looks like. How many diagonals does a polygon with 16 sides have? Hexagon. Learn the hexagon definition and hexagon shape. Before using counting tools, we need to know what we are counting. What is the area of a regular hexagon inscribed in a circle of So, the area of hexagon will be 6 times this area because the hexagon is divided into 6 equilateral triangles. If all of the diagonals are drawn from a vertex of a quadrilateral, how many triangles are formed? We have 2 triangles, so 2 lots of 180. In each of the following five figures, a sample triangle is highlighted. This same approach can be taken in an irregular hexagon. How many vertices does a triangular prism have? How are relationships affected by technology? A regular octagon is an example of a convex octagon. You have 2 angles on each vertex, and they are all 45, so 45 8 = 360. How many different types of triangles can be formed with the vertices of a balanced hexagon? for 1 side we get (n-4) triangles $\implies$ n (n-4) triangles for n sides. The interior angles of a triangle always sum to 180. Where A means the area of each of the equilateral triangles in which we have divided the hexagon. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. 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 area of the hexagon is 24a2-18 square units. 1. The number of triangles is n-2 (above). Indulging in rote learning, you are likely to forget concepts. Since the interior angles of each triangle totals 180, the hexagon's interior angles will total 4(180), or 720. A: 209 diagonals So, a polygon with 22 sides has 209 diagonals. of triangles corresponding to one side)}\text{(No. Is it suspicious or odd to stand by the gate of a GA airport watching the planes? Total of 35 triangles. Total number of such triangles$=nC1*(n-4)C1$, [By $nC1$ we are choosing any side of the polygon(which is going to be a side of the triangle) and by $(n-4)C1$ we are choosing the vertex of triangle opposite to the line chosen.There we have used $(n-4)$ as the points on the line and the neighbouring points are excluded,because we are not dealing with two common sides here]. You will notice that with one or two chopsticks, for example, it is impossible to form a triangle, and that with three chopsticks only one triangle can be formed: While with 11 chopsticks four different triangles can be formed. What is the purpose of this D-shaped ring at the base of the tongue on my hiking boots? When you create a bubble using water, soap, and some of your own breath, it always has a spherical shape. 3! 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. How many segments do a 7 sided figure have joined the midpoints of the sides? Convex octagons are those in which all the angles point outwards. With two diagonals, 4 45-45-90 triangles are formed. How many sides does a regular polygon have? For a full description of the importance and advantages of regular hexagons, we recommend watching this video. The perimeter of the hexagon formula is simply: Area = 1/2 x perimeter x apothem. For the sides, any value is accepted as long as they are all the same. 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 . @Freelancer you have $n$ choice of sides. If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed? The next case is common to all polygons, but it is still interesting to see. How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm? Math can be daunting for some, but with a little practice it can be easy! The easiest way to find a hexagon side, area Hexagon tiles and real-world uses of the 6-sided polygon, Honeycomb pattern why the 6-sided shape is so prevalent in nature. G is the centre of a regular hexagon ABCDEF. case II, 3) triangles with no side common Do new devs get fired if they can't solve a certain bug? 3 This rule works because two triangles can be drawn inside the shapes. 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. Thus, those are two less points to choose from, and you have $n-4$. The interior angle at each vertex of a regular octagon is 135. It should be no surprise that the hexagon (also known as the "6-sided polygon") has precisely six sides. Thus, 6 triangles can come together at every point because 6 60 = 360. Using a common vertex, and with the help of diagonals, 6 triangles can be formed in an octagon. Try to use only right triangles or maybe even special right triangles to calculate the area of a hexagon! In photography, the opening of the sensor almost always has a polygonal shape. Proof by simple enumeration? Hence no of triangles= n 3! 10 triangles made of 3 shapes. Check out 23 similar 2d geometry calculators , How many sides does a hexagon have? Triangle = 3 sides, 0 diagonal, 1 triangle, 2.) If all of the diagonals are drawn from a vertex of an octagon, how many triangles are formed? Correct option is A) Since decagon has 10 sides, clearly 10 vertices of decagon say A 1,A 2,A 3,.,A 10. This is interesting, @Andre considering the type of question I guess it should be convex-regular. 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. 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. Yes you create 4 triangles with a sum of 720, but you would have to subtract the 360 that are in the middle of the quadrilateral and that would get you back to 360. $\implies$ can also be written as sum of no of triangles formed in the following three cases, 1) no of triangles with only one side common with polygon, In a convex 22-gon, how many. Since a regular hexagon is comprised of six equilateral triangles, the. How many parallelograms are in a hexagonal prism? How many degrees is the sum of the measures of the interior angles of a regular polygon with 18 sides? In case of an irregular octagon, there is no specific formula to find its area. Thus, there are 20 diagonals in a regular octagon. How many triangles can be formed with the given information? To determine the area of a hexagon with perimeter P: You could also go directly from P to the area by using the formula area = 3 P / 24. 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. Now, the 11 vertices can be joined with each other by 11C2 ways i.e. 6 triangles can be formed in a regular octagon with the help of diagonals using a common vertex. How many triangles make a hexagon? a) 5 b) 6 c) 7 d) 8. if triangle has a perimeter of 18, what is the perimeter of hexagon? These cookies ensure basic functionalities and security features of the website, anonymously. How many obtuse angles does a square have? One of the biggest problems we experience when observing distant stars is how faint they are in the night sky. Since the interior angles of each triangle totals 180, the hexagon's interior angles will total 4(180), or 720. Discover more with Omni's hexagon quilt calculator! 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. This same approach can be taken in an irregular hexagon. 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. https://www.youtube.com/watch?v=MGZLkU96ETY. Writing Versatility. When all else fails, make sure you have a clear understanding of the definitions and do some small examples. Therefore, number of triangles = 6 C 3= 3!3!6! The solution is to build a modular mirror using hexagonal tiles like the ones you can see in the pictures above. You count triangles that way. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The inradius is the radius of the biggest circle contained entirely within the hexagon. The number of inverted triangles with a peak in the downward direction of size K present in size N equals to ( (N - 2K + 1) * (N - 2K + 2))/2. The sum of the interior angles of an octagon is 1080, and the sum of its exterior angles is 360. The sum of exterior angles of an octagon is 360. I got an upgrade, but the explanations aren't very clear. The area of a triangle is \displaystyle 0.5\cdot b\cdot h. Since, How to determine greatest common monomial factor, How to find the height of a trapezium calculator, How to find the mean of a frequency distribution chart, Post office term deposit interest calculator, Va disabilty rate calculator with bilateral factor. However, when we lay the bubbles together on a flat surface, the sphere loses its efficiency advantage since the section of a sphere cannot completely cover a 2D space. 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? The angle bisectors create two half angles which measure 60: mOAB=mOBA=60. Therefore, 8*9*7= 336 there are possible triangles inside the octagon. If all of the diagonals are drawn from a vertex of a pentagon, find how many triangles are formed. When you imagine a hexagon as six equilateral triangles that all share the vertex at the hexagon's center, the apothem is the height of each of these triangles. How many diagonals can be formed by joining the vertices of the polygon having 5 sides? c. One triangle. This is called the angle sum property of triangle. We know that in a regular octagon, all the sides are of equal length. This fact makes it much easier to calculate their area than if they were isosceles triangles or even 45 45 90 triangles as in the case of an octagon. if we take any one side of a n-sided polygon and join its vertices to the remaining vertices, except the vertices adjacent to vertices of the line taken above, we get triangles with only one side as common i.e. How many triangles can be formed with the vertices of a regular pentagon? There will be a whole section dedicated to the important properties of the hexagon shape, but first, we need to know the technical answer to: "What is a hexagon?" 0 0 Similar questions Sides No. Therefore, 6 triangles can be formed in an octagon. The sum of all the exterior angles in an octagon is always 360. 2) no of triangles with two sides common, The perimeter of a hexagon can be calculated Passing Rate Deal with math problem Solve math equation . 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. Number of triangles contained in a hexagon = 6 - 2 = 4. If we draw the other four missing chords and the one missing radius, we obtain too many triangles to count (I stopped at thirty). One triangle is formed by selecting a group of 3 vertices from the given 6 vertices. An equilateral triangle and a regular hexagon have equal perimeters. This cookie is set by GDPR Cookie Consent plugin. Another important property of regular hexagons is that they can fill a surface with no gaps between them (along with regular triangles and squares). 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. In a regular hexagon, four triangles can be created using diagonals of the hexagon from a common vertex. Solve word questions too In addition to solving math problems, students should also be able to answer word questions. The perimeter of an octagon is the total length of its boundary. Example 2: Find the length of each side of a regular octagon if the perimeter of the octagon is 160 units. 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). So, the total diagonals will be 6 (6-3)/2 = 9. Did you know that hexagon quilts are also a thing?? 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. How many diagonals are in a pentagon, an octagon, and a decagon? Number of triangles contained in a hexagon = 6 - 2 = 4. case I The diagonals of an octagon separate its interior into 6 triangles Properties of regular octagons Symmetry The regular octagon features eight axes of symmetry. 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. 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. What is the number of triangles that can be formed whose vertices are the vertices of an octagon? Octagon is an eight-sided two-dimensional geometrical figure which consists of 8 interior angles and 8 exterior angles. The formula to calculate the area of a regular hexagon with side length s: (3 3 s^2)/2. How many diagonals are in a 100-sided shape? How many distinct equilateral triangles exist with a perimeter of 60? C. How many right angles does a hexagonal prism have? Thus, for each of the 8 vertices you can draw 5 diagonals and hence there can be 5 8 = 40 diagonals. Thus there are $(n-4)$ different triangles with only one side $A_1A_2$ common. As for the angles, a regular hexagon requires that all angles are equal and sum up to 720, which means that each individual angle must be 120.