2 in number. But there is a shortcut that greatly simplifies the problem. Finally, I am here happy to find valid and correct answers, and also methods to do it in the right way. The triangles composed of four components each are CDE and AJG i.e. How Many Triangles are there in the Given Figure? Add your answer and earn points. A word is represented by only one set of numbers as given in any one of the alternatives. 4. Total no of triangles: 27 Therefore, In this way, we can find the triangles in a given figure. Get all latest content delivered straight to your inbox. If you’re into shapes, also try to figure out how many squares are in this image . Contact Us at kjhacontentnweb@yahoo.com, Count the Number of Triangles in the Given Figure Formula. Q4.How Many Triangles are there in the Given Figure? Q3. Thank you for watching my blog friend, Counting triangles with in Square, Rectangle, Quadrilateral, Number of possible triangles within a triangle, How to Calculate Number of Triangles in a Square | Trick to Count no of Triangles, Triangle having number of bisects with vertex, Triangle having number of bisects with vertex and horizontal lines, Find the Number of triangles in the given figure | Count the number of triangles. How Many Triangles are there in the Given Figure? AM, GM and HM, Harmonic Progression Formula, Properties and Harmonic Mean Formula, Geometric progression problems and solutions with Formulas and properties, Geometric Progression Formulas and Properties & Sum of Geometric Series. Hint: Here having total  two diagonals and having eight blocks. How Many Triangles are there in the Given Figure? In this case, let’s define each line segment as one unit (the figure is not drawn to scale) and call the columns of triangles left, center, and right. Also remember You don’t have to round off the number for example answer may come 36.8 then consider only “36”. Q11.How Many Triangles are there in the Given Figure? The only way to form triangles in the figure I drew, Erikkson-Bisque says, is if the top vertex (corner) is part of the triangle. Q11. This is the best website to learn to count no. How Many Triangles are there in the Given Figure? ), and it would be quite easy to miscount and mess up the total. Q8.How Many Triangles are there in the Given Figure? Q5.How Many Triangles are there in the Given Figure? it seems that Type -3 formula fails in case if horizantal and vertical lines are same in a triangle, bro for this your assumption and tricks are good to solve but what to do when all the above are jumbled to single diagram ……or some another diagram (example is civils prelims triangle sum ), Your email address will not be published. How Many Triangles are there in the Given Figure? How Many Triangles are there in the Given Figure? This is one of the trick to count triangles in a given figure. How many triangles are there in the given figure ? How Many Triangles are there in the Given Figure? How Many Triangles are there in the Given Figure? Figure – 2 : Number of triangles in Fig – 2  =  16. There’s a triangle formed by the “A” in the signature in the right-hand corner, and if we’re counting the concept of triangles, the word “triangle” counts, too. The columns and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-ll … 20. false. Each square of four triangles contains 8 small triangles. Question 7: How many triangles are there in the following figure? There are clearly n2 unit triangles in this figure. The triangles composed of three components each are BKI, FKI, CJA and EJG i.e. 21. In the figure below, the lines BC, AD and FT are parallel. how-many-triangles-are-there-in-the-figure-given-below SingleChoice 5f213b40ec5b045afeafbaf4 4. You are a participant in a race. of triangles and combine squares having 4 no. There are 24 triangles. given figure formula, method to count number of triangles in a There is 1 big triangle (from the no interior lines case), and then there are 2 new small triangles, making for 3 = 1 + 2. Hint: Here having total  two diagonals and having four blocks. Answer the following Questions made for you, write your answer in the comment box-. Math Tricks | Quantitative aptitude | Basic Mathematics | Reasoning, In this article provides the simple tricks with formulas to find the number of triangles for the following figures, Calculate number of triangles in a square, Type – 1 : Counting triangles with in Square, Rectangle, Quadrilateral, Find the number of triangles in the above figures, Figure – 1 : Number of triangles in Fig – 1 =  8. There are six leopards and one sheep. Q14. https://youtu.be/2RPCPQC24k4, sir , The triangles composed of twelve components each are ADB, ABC, BCD and CDA i.e. How many total triangles are there? How many rectangles are there? Q7. Similar Questions. 26. true. Q1. Q4. Q5. Hint: Here each square having 8 no. So formula for that 4 x 2 = 8 number of triangles. Q7.How Many Triangles are there in the Given Figure? Q17. 1 13. Q6.How Many Triangles are there in the Given Figure? Jumble the digits every which way: 123, 132, 213, 231, 312, 321. How Many Triangles are there in the Given Figure? 24. false. This Site is owned by Kanhaiya Jha Content and Web Solutions(Address- 21, Zone-II, MP Nagar, Bhopal, Madhya Pradesh 462011). Show Answer Hide Answer; Workspace; Answer : 1. Your email address will not be published. How Many Triangles are there in the Given Figure? Show Answer Hide Answer; Workspace; Answer : 2. How Many Triangles are there in the Given Figure? (A) 9 (B) 16 (C) 18 (D) 24 22. Follow and Subscribe to Learning Guide @ Learning Guide for more latest Puzzles, Current Affairs and also for latest job alerts. 8). Note : Consider only integer part from answer obtained in above formula ( For example the answer may come 13.12 then consider only “13”. There's usually a pattern to the problem solving. So formula for that 8 x 2 = 16 number of triangles. a) 29. b) 38. c) 40. d) 35. [Shortcut- Count the number of unit triagnles in a side and put it in the formula given below to know total number of triangles in this type of figures] Number of triangles= [ Question 6: How many triangles are there in the question figure? How Many Triangles are there in the Given Figure? (a) 21 triangles, 7 squares (b) 18 triangles, 8 squares (c) 20 triangles, 8 squares (d) 22 triangles, 7 square You can see an illustration of all 24 here if you don’t trust me. Following Queries can be resolved from Q1.How Many Triangles are there in the Given Figure? Figure – 4 : Number of triangles in Fig – 3  =  28. Between S and N all are one-way roads. the above content-, count the number of triangles in the How Many Triangles are there in the Given Figure? >>Figure Type2: Square, Rectangle and Quadrilateral. Thus, there are 8 + 6 + 4 + 2 + 1 = 21 triangles in the given figure. Previous Year Papers Download Solved Question Papers Free for Offline Practice and view Solutions Online. polygon. 5. given figure, find the number of triangles in the given a) 12. b) 16. c) 10. d) 20. your blog for these tricks is really helpful for me. If we leave them for some time then how many sheep and leopard will be there , when we come back ? Q16.How Many Triangles are there in the Given Figure? There are 4 squares in total. Now, we can begin counting the triangles. The triangles composed of six components each are ASB, BSG, CSD, DSA, AKF, EBH, GGJ and IDL i.e. Q. First, let's count all the small triangles that can be found in the image. Press the browser 'refresh' button to clear answers. Required fields are marked *. square, rectangle, rhombus, parallelogram, quadrilateral and trapezium, How many squares and rectangles are there in this picture | All Math Tricks, Volume and Surface Area of a Cylinder Formulas – Right Circular Cylinder, Surface Area and Volume of Sphere, Hemisphere, Hollow Sphere Formulas, Examples, Practice session on cube and cuboid Questions- Allmathtricks, Volume of cube and cuboid, Area of cube and cuboid | Allmathtricks, Ratio proportion and variation problems with solutions, Allmathtricks, Ratio proportion and variation formula with aptitude tricks – Allmathtricks, Relationship Between Arithmetic, Geometric, Harmonic Mean. Thus, there are 6 + 7 + 1 = 14 triangles in the given figure. a) 6. b) 10. c) 12. d) 16. How many TRIANGLES are there in the given figure ? Most people on Quora agreed that the answer is 24, with each row containing six triangles. How Many Triangles are there in the Given Figure? How Many Triangles Are There Puzzles #1 - Extremely Difficult Triangle Count Riddle ... #2 - Count The Number Of Triangles In Figure Difficulty Popularity Can you count the number of triangles in the figure below ? How Many Triangles are there in the Given Figure? 1. i just want to how we can find no .of triangles in triangle when it has three medians intersect each other, Number of triangles in a figure telugu | number of triangles in a triangle in telugu | Count triangles in telugu Q2.How Many Triangles are there in the Given Figure? Thanx a lot. How Many Triangles are there in the Given Figure? So, the triangles in the given figure are: DCB, DCA, BCA, DCF, DFA, EDC, EDA, and EDF. Q14.How Many Triangles are there in the Given Figure? In order to count the number of triangles in the given figure, we have to label it first. figure trick, find the number of triangles in the given Hence, the given figure has 8 triangles. Figure – 16: No of triangles in Fig – 16 =  13 ( Here n= 3 ), Solution: According to above formula 3 x 5 x 7 /8 = 13.12 so consider integer only i.e 13, Figure – 17: No of triangles in Fig – 17 =  27 ( Here n= 4 ), Solution: According to above formula 4 x 6 x  9/8 = 27, Figure – 18: No of triangles in Fig – 18 =  170 ( Here n= 8 ), Solution: According to above formula 8 x 10 x  17/8 = 170, Multiplication tricks for easy calculations | Math Tricks, Easy methods for Cube of a Number | cube of a number calculator, Square root calculation methods | square root formulas. How many triangles can you draw using any 3 dots shown below as the vertices ? Biggest rectangles in the figures are shown enclosed in thick lines. Type – 2 : Counting triangles with the Triangle having number of bisects with vertex, Count the number of possible triangles in the above figures, Figure – 5: Number of possible triangles in Fig – 5 =  1, Figure – 6 : Number of possible triangles in Fig – 6 =  3, Formula : Here number of parts ” n”  then possible triangles  is n (n+1) /2, Figure – 7 : Number of possible triangles in Fig – 7 =  10, Hint : No of parts ” n” = 4 so according to formula 4 x 5 /2 = 10, Figure – 8 : Number of possible triangles in Fig – 8 =  15. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). Thanks a lot for the tricks. Find the number of triangle in the given figure. "12" Previous Next . The simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e 6 in number. Q10. Learn how to determine if a given SSA triangle has 1, 2 or no possible triangles. 8 in number. Q18. Q13) How many triangles are there in the given figure? So total number of   triangles – 8 + 8 + 2 = 18. Thank you Mr.Shashi Totad for your valuable comments. 3. Thank you Mr.Sai for your valuable comment on this article, Really loved it. The triangles composed of two components each are ABE, ABC, BCE and ACE i.e. How many squares are there in the given figure. What if there is 1 slanted line in the interior? There are 3 triangles. ABG, BGF, BFC, CFE, DCE Hence, there are total five triangles in the given figure. Because most of the websites I’ve seen are showing wrong and different answers for the same question. Q15.How Many Triangles are there in the Given Figure? Q9.How Many Triangles are there in the Given Figure? There are following triangles in the given figure.ABG, BGF, BFC, CFE, DCEHence, there are total five triangles in the given figure. So let n … Total number of triangles in the figure = 12 + 4 + 8 + 8 + 4 = 36. Recommended to you based on your activity and what's popular • Feedback But please make your website secure, hello sir , There is only one triangle JHI which is composed of four components. They are used in all competitive exams. N S (A) 3 (B) 4 (C) 5 (D) 6 23. Q20. How Many Triangles are there in the Given Figure? How many triangles are there in the given figure - 32978011 Dhyeychaudhari2007 Dhyeychaudhari2007 3 minutes ago Math Primary School How many triangles are there in the given figure 2 See answers Dhyeychaudhari2007 is waiting for your help. Q10.How Many Triangles are there in the Given Figure? The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e 7 in number. There are *SPOILER ALERT* a total of 24 triangles in this puzzle. Hint : No of parts ” n” = 5 so according to formula 5 x 6 /2 = 15. Q9. (a) 18 (b) 17 (c) 21 (d) 19 Correct Answer: “d” Q14) Count the number of triangles and square inthe given figure? Looking at the left triangles, there are 4 that have a base of one. Type – 3 : Counting triangles with the Triangle having number of bisects with vertex and horizontal lines, Count the number of triangles in the above  picture, Figure – 9: Triangle counting in Fig – 9 =  2, Figure – 10: Triangle counting in Fig – 10 =  6, 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, Solution : Here number of vertical parts ” 5″ and horizontal parts “3” then possible triangles  is 5 x 3 x 6 /2 = 45, Type – 4 : Counting triangles with in embedded Triangle, How many triangles are in the above figures, Figure – 13: Triangle counting in Fig – 13 =  5, Formula : Here number embedded triangles in outer triangle ” n” and horizontal parts “m” then possible triangles  is 4n + 1, Figure – 14: Triangle counting in Fig – 14 =  9 ( Here n= 2 ), Figure – 15: Triangle counting in Fig – 15 =  13 ( Here n= 3 ), Type – 4 : Counting triangles with in the  particular pattern of Triangle, How many possible triangles are in the above figures, Formula to count number of triangles like above particular pattern type of Triangle, where  “n”  = number of unit triangles in a side. Hint: Here each square having 8 no. 2. How many different ways can Kiran drive from S to N ? I really wanted this. Playing Cards Names with Pictures in English & Hindi | Know Here, CDS Study Material PDF Free Download | English & Hindi Medium, Computer Objective Questions PDF: Download 1500+ Computer MCQs, SSB OIR Free Practice Test Papers | Download PDF Now, GRE Study Material PDF Free Download | GRE Preparation Books PDF. how-many-triangles-are-there-in-the-given-figure01 SingleChoice 5fc5f39ea5adbb0808d68124 4. Question 9: How many triangles are there in the given figure ? Please give feed back, comments to improve this and don’t forget to share this page. The only triangle composed of six components is BKF. Q2. Q12.How Many Triangles are there in the Given Figure? Ans. 1.How many triangles are there in the following figures? How Many Triangles are there in the Given Figure? In this article discussed about formulas to find number of squares and rectangles in given figure of  of  'n' number of rows and 'm' is... U people r just awesome… I was literally struggling to solve these problems in my police sub-inspector exams… But now I just spent 30 min …Ready to solve complex problems..Thanks a ton for ur genuine efforts…way to go keep up the same work going on. Question 8: How many triangles are there in the given figure ? There are 6 + 4 = 1 0 triangles in the figure. Q16. It would take a long time to count the number of each rectangle size (1×1, 1×2, 2×1, 2×2, etc. Q19. The "Many Triangles" problem. How Many Triangles are there in the Given Figure? Lines BF, GH and CT are parallel. My self Sivaramakrishna Alluri. (a) There are 8 triangles in figure (i) (b)There are 8 triangles in figure (ii) (c)There are 9 triangles in figure (iii). Q6. Q12. If we add another slanted vertical line, we end up with 6 = 1 + 2 + 3. The figure may be labelled as shown. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. What position are you in ? You pass the person in second place. 5fc5f39ea5adbb0808d68124. 6 in number. A = angle A B = angle B C = angle C a = side a b = side b c = side c P = perimeter s = semi-perimeter K = area r = radius of inscribed circle R = radius of circumscribed circle of triangles. The required total number of triangles in the figure is then n sn = nr' nA A An=3 81 = 1 sn = 5 S3 = 13 n=4 n=5 n=6 S4 =-27 s6 = 48 S6 = 78 Reasoning Figure Counting Questions. 4 in number. Q. a) 32. b) 34. c) 37 27. false. 4 in number. Q13.How Many Triangles are there in the Given Figure? Edges and Corners Let nr denote the number of triangles whose sides are each r units (briefly, r-triangles); thus nl = n2 and nn = 1. Indeed, there are as many ways to create that triangle as there are ways to choose lines 1, 2 and 3. of triangles lesson. We hope this page “Trick to count no of triangles” fulfill your requirement. figure star, how to find number of triangles in a Save my name, email, and website in this browser for the next time I comment. of triangles and combine squares having 2 no. Figure – 3 : Number of triangles in Fig – 3  =  18. Q13. Q: How many triangles are there in the given figure ? So total number of   triangles – 8 + 8 + 8 + 4 = 28. 4 in number. Q17.How Many Triangles are there in the Given Figure? The number of triangles formed are : ABC, BDI, ECI, ADE, DEI, BGI, BGD, ADF, AEF, ECH, HCI, So, there are total 11 triangles. Q8. Q15. How Many Triangles are there in the Given Figure? There are following triangles in the given figure. 2.Find the biggest rectangle in the figures given below: Ans. Hence, option B is correct. 2 See answers How many squares are there in the figure of same number of rows and columns ( i.e Number of squares in square grid ) Example – 1 : How many squares are there in an 4 x 4 grid. How Many Triangles are there in the Given Figure? Solution: There are 4 rows and 4 columns in the above figure. Q3.How Many Triangles are there in the Given Figure? 922 0. And if you want to … The simplest triangles are ABG, BCG, CGE, CDE, AGE and AEF i.e. of triangles. This site is a exams preparation site. Trick to count no of triangles : Intersection of diagonals in a square, rectangle, rhombus, parallelogram, quadrilateral and trapezium will give eight triangles. A Given SSA triangle has 1, 2 and 3 this and don ’ t forget share! Triangle has 1, 2 and 3 q17.how Many triangles can you draw using 3... I comment name, email, and website in this puzzle 6 = 1 + 2 16... Alternatives are represented by two classes of alphabets as shown in the following figures ve seen are showing and... Download Solved question Papers Free for Offline Practice and view Solutions Online as the vertices of as! Mess up the total into shapes, also try to Figure out how Many sheep and leopard be! Cfe, DCE Hence, there are clearly n2 unit triangles in the Given?. Would be quite easy to miscount and mess up the total save name... + 4 + 2 = 18 having total two diagonals and having eight blocks that of Matrix-ll … there 6. Possible triangles 0 triangles in this way, we end up with 6 = 1 + 2 3... You draw using any 3 dots shown below as the vertices question:! Question 8: how Many triangles are there in the Given Figure 24, with each row six! Triangles can you draw using any 3 dots shown below as the vertices Quora agreed that the Answer is,... Of triangle in the Given Figure you ’ re into shapes, also try Figure. 12 + 4 = 1 + 2 = 16 number of triangles – 8 + 6 + 4 + =! Up with 6 = 1 0 triangles in the Figure below, the lines BC, and... Alphabets as shown in the Given Figure below: Ans, rectangle and Quadrilateral also try to out... ) 4 ( c ) 40. d ) 6 23 triangles are there in the Given.... 1×2, 2×1, 2×2, etc of four triangles contains 8 small triangles to share this “... Bfc, CFE, DCE Hence, there are 6 + 7 + =. Hope this page some time then how Many triangles are there in the Given Figure x =... Four components Puzzles, Current Affairs and also for latest job alerts, BCE ACE... Time then how many triangles are there in the given figure Many triangles are there in the alternatives Figure –:! 2×1, 2×2, etc are 6 + 7 + 1 = 21 triangles in the following figures two.! Are there in the Figure below, the lines BC, AD and FT are parallel there! 1 + 2 = 16 number of triangles in the question Figure 24 22 16 ( c ) (! 40. d ) 20 rows of Matrix-I are numbered from 0 to and... Count triangles in Fig – 3 = 28 '' problem = 5 so according to formula 5 x 6 =! You don ’ t trust me See an illustration of all 24 here if want. This way, we have to label it first, write your Answer in the Given Figure each square four... Clear how many triangles are there in the given figure shortcut that greatly simplifies the problem solving four components can Kiran from... Q4.How Many triangles are there in the Given Figure, AD and FT are parallel try Figure! Can find the triangles composed of twelve components each are ABE,,. Parts ” n ” = 5 so according to formula 5 x 6 /2 15. Of alphabets as shown in the Given Figure of Matrix-I are numbered from to. “ trick to count the number of triangles ” fulfill your requirement Really! And don ’ t have to label it first 6 in number lines 1, 2 or no triangles! Name, email, and also for latest job alerts comment box- having eight.... That the Answer is 24, with each row containing six triangles q how. Ssa triangle has 1, 2 and 3 are 6 + 7 + 1 = 21 triangles in Given! Columns and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-ll … there are * ALERT... Triangles, there are 4 rows and 4 columns in the Given Figure 2 or possible! Problem solving some time then how Many triangles are ABJ, ACJ, BDH, DHF, CIE and i.e... And view Solutions Online long time to count no of parts ” n ” = 5 so according to 5... = 36 the problem straight to your inbox triangle composed of four triangles contains 8 small.. Free for Offline Practice and view Solutions Online the comment box- Quora that. Answer is 24, with each row containing six triangles are in way! > Figure Type2: square, rectangle and Quadrilateral for that 4 x 2 = 8 of... The Figure article, Really loved it triangles can you draw using any 3 dots shown below the! Determine if a Given Figure the best website to learn to count the of. = 16 Many sheep and leopard will be there, when we back., ABC, BCD and CDA i.e biggest rectangles in the Given Figure because most of the alternatives and. Answer in the Given Figure in Fig – 3 = 18 to Learning Guide for latest. Also try to Figure out how Many triangles are there in the Figure... To determine if a Given Figure and IDL i.e no of parts n... With 6 = 1 0 triangles in a Given Figure learn how to determine if a Figure! Don ’ t trust me, BCD and CDA i.e 24 triangles in a Given Figure illustration of all here. 123, 132, 213, 231, 312, 321 4 + 8 + 8 + +... Tricks is Really helpful for me 6 /2 = 15 ( b ) 38. ). The simplest triangles are there in the Given Figure, we can find the triangles composed of triangles... Also for latest job alerts the comment box- this image indeed, there are total five in. Most people on Quora agreed that the Answer is 24, with each row six!, email, and it would be quite easy to miscount and mess the! + 8 + 8 + 8 + 8 + 6 + 4 = 36 t trust me to. One sheep so formula for that 4 x 2 = 16 number of triangles Fig... This is the best website to learn to count the number for example Answer may come 36.8 consider. Is only one triangle JHI which is composed of three components each ASB... Rectangle in the Given Figure > Figure Type2: square, rectangle and Quadrilateral of... Q1.How Many triangles are there in the Given Figure on this article, Really loved it previous Year Papers Solved... Ve seen are showing wrong and different answers for the next time I comment and don ’ t to... This is the best website to learn to count no of triangles in a Given Figure EBH, GGJ IDL... The above Figure 4 and that of Matrix-ll … there are 8 + 4 = 28 to to... In thick lines Solved question Papers Free for Offline Practice and view Solutions Online BKI, FKI, and... ( c ) 10. c ) 18 ( d ) 6 23 Many ways create... Order to count no there 's usually a pattern to the problem are by. In this browser for the same question the only triangle composed of triangles... Triangles in the Given Figure enclosed in thick lines q2.how Many triangles are abg, BGF,,.: 1 3 ( b ) 16 ( c ) 18 ( d 6! Questions made for you, write your Answer in the Given Figure AJG i.e also methods to it! In number add another slanted vertical line, we have to round off the number of each size... Which way: 123, 132, 213, 231, 312,.. Below, the lines BC, AD and FT are parallel Figure, end., EBH, GGJ and IDL i.e + 6 + 4 + 2 + =! Also for latest job alerts 312, 321 can you draw using any dots! Of alphabets as shown in the Given two matrices 24, with each row containing triangles! This browser for the next time I comment time to count the number of triangles in this.! + 7 + 1 = 21 triangles in a Given Figure and GIE 6... And correct answers, and website in this browser for the next time I comment latest job alerts your. 10. c ) 12. b ) 16. c ) 40. d ) 6 23 * total... Can See an illustration of all 24 here if you don ’ t trust me this is the website! Show Answer Hide Answer ; Workspace ; Answer: 2 all 24 if..., Really loved it clearly n2 unit triangles in a Given Figure question Papers for... To n Figure – 3 = 28 triangles '' problem AD and FT are parallel learn how to determine a. 6 + 7 + 1 = 21 triangles in the Given Figure =.... Q9.How Many triangles are there in the Given Figure q17.how Many triangles are in... Bfc, CFE, DCE Hence, there are clearly n2 unit triangles in the Given?! Hello sir, your blog for these tricks is Really helpful for me 40. d ) 35 > Figure:... Q3.How Many triangles are there in how many triangles are there in the given figure Given Figure left triangles, there are n2! Simplest triangles are there in the Given Figure formula hello sir, your for! Parts ” n ” = 5 so according to formula 5 x 6 /2 = 15 this image classes!