What is Trapezoid: Definition and 44 Discussions

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezium () in English outside North America, but as a trapezoid () in American and Canadian English. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides (if they are not parallel; otherwise there are two pairs of bases). A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast with the special cases below.
The shape is found frequently in nature, for example the human trapezius muscles and the acrobatic trapeze.

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  1. kfulton

    Distance with Trapezoid Rule

    Here is the problem in it form with chart. The answers are written in and we needed to verify they were correct. We were told they were correct, but I am not getting that answer. I start with 5-0/2 (5)(18). I thought that was first stop and I was way wrong. Not sure how else to do to get the...
  2. Tom Hammer

    Supporting a trapezoid between two wedges

    Let Nr = normal force on the right side of the trapezoid B and Fr = the force of friction on the right side of B. Let Nl = normal force on the left side of B and Fr = the frictional force on the left surface of B so Nr = 5 sin45 and Fr = 5 sin45 = and Nl = 5 sin 60, Fl = 5 sin 30.
  3. J

    MHB Finding the Length of a Dividing Line in a Trapezoid

    A trapezoid with a base of 100m and 160m is divided into 2 equal parts by a line parallel to the base. Find the length of dividing line.
  4. C

    Trapezoid method converges faster than the Simpson method

    Good Morning, I have been doing computer practices in C ++, and for an integration practice, the trapezoid method converges faster than the Simpson method. The function to be integrated is a first class elliptical integral of the form: Where k is bounded between [0,1). I have been thinking...
  5. Trapezoid Area Formula Origin

    Trapezoid Area Formula Origin

    How trapezoid's area formula came to be.
  6. ISamson

    Finding height and area of trapezoid from its legs and bases

    Hello. I am wondering how I can find the area of a trapezoid from its two legs and bases. My problem: ABCD is a trapezium with AB parallel to CD such that AB = 5, BC = 3, CD = 10 and AD = 4. What is the area of ABCD? If we trace a straight line from A down parallel to the height of the...
  7. starstruck_

    Related rates (prism with a trapezoid base)

    Homework Statement A trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm. If the trough is being filled with water at the rate of 0.2m3/min, how fast is the water level rising when the...
  8. J

    Maximum velocity for the motor movement

    Hello all, First of all let me say this is my first post here and I don't know if I'm placing it into the right forum/place. If I'm doing something wrong or similar, please let me know and I'll try to solve it asap. This is not homework, but it is for sure introductory level so I've thought...
  9. M

    A Laplace equation on a trapezoid

    Hello everybody! I know how to solve Laplace equation on a square or a rectangle. Is there any easy way to find an analytical solution of Laplace equation on a trapezoid (see picture). Thank you.
  10. magnetpedro

    Area of trapezoid formed by slicing a cylinder

    What is the equation of the area of the trapezoid when a cylinder of radius R is cut by a plane inclined at an angle α? (Orange area of the figure) How can I relate it with Abase=π*R2 or with Ainside=2*R*L? Any hints please? Thank you very much in advance.
  11. B

    Calculate Trapezoid Current: Formula & Explanation

    may i know what is the formula to calculate current of trapezoid??
  12. L

    Utilize the Trapezoid Rule for e^cosx, and find the error

    Homework Statement Consider the definite integral, from 0 to 4, e^(cosx) dx a) Compute the estimate for this integral using the trapezoid rule with n = 4. b) Find a bound for the error in part a. c) How large should n be to guarantee that the size of the error in using Tn is less than 0.0001...
  13. J

    MHB Solve Circle Radius Given Trapezoid Height & Length

    I don't know if this can be calculated. I have tried for hours and days to isolate/calculate the radius and angles of the circle in order to be able to calculate length 1. I have tried using cos/sin-relation formulas and triangle formas - but Iam stuck. Any hints would be greatly appreciated...
  14. L

    MHB Can Thales' Theorem Help Me Solve My Trapezoid Equation?

    I have the above equation to try and complete and I have no idea how to do it I have worked out all the angles for A, B, C, and D accept the ones within the diagonal line E and F. Any hints?
  15. J

    MHB Trapezoid & Simpson's Rule with their respective errors.

    Hey Everyone, I know I just posted yesterday, but I have another problem from the first chapter of my Calc 2 summer course that I would like to iron out. Integral of (5/x)dx from 1 to e with n=4, 8 finding both Trapezoid rule and Simpson's rule approximations, and their errors. I know how to...
  16. S

    MHB Verifying Int. of f(x) Using Trapezoid Rule

    Just need someone to verify my solution and that I have done my calculations correctly. Thank you again for all of your help in advance, everyone on this forum has helped me SO much with my classes this semester. Using the trapezoid rule. The following data was collected about the function...
  17. Albert1

    MHB Finding $\dfrac{AC}{BD}$ of a Trapezoid $ABCD$

    A trapezoid $ABCD$ , $BC//AD ,\,\, \angle A=90^o$ , $AC\perp BD$ given :$\dfrac {BC}{AD}=k$ find :$ \dfrac {AC}{BD}$
  18. MarkFL

    MHB Maximize Trapezoid Area with 3 Equal Sides | Leprofece Answer

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  19. I

    Error of Simpson's, Trapezoid, etc. Rules

    I learned this a while ago in my calculus 2 class and I was just thinking about it... Where do these error equations for each of the approximation rules come from? Like for example, where does the error for the Simpson's rule, $$|E_{S}|\le \frac{M(b-a)^{5}}{180n^{4}}$$ come from? Also, why even...
  20. MarkFL

    MHB Maximize Area of Isosceles Trapezoid: Solve w/ Maxima & Minima

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  21. Albert1

    MHB Find Area of Trapezoid ABCD | $(\sqrt 3+1):(3-\sqrt 3)$

    A trapezoid ABCD ,AD // BC ,points E and F are midpoints of AB and CD respectively (1)area AEFD :area EBCF =($\sqrt 3+1) : (3-\sqrt 3)$ (2) area of $\triangle ABD=\sqrt 3$ please find the area of ABCD
  22. Albert1

    MHB Can you find the area of a trapezoid with four given side lengths?

    1,2,3,4 are four side length of a trapezoid,please find the area of this trapezoid
  23. R

    Calculate Constant Velocity & Speed for Trapezoid Move

    Hi All, A question to calculate the speed at constant velocity during a Trapezoid move. An object moves from standstill at a known acceleration (1m/s/s) to a constant velocity (unknown) for a period (unknown) and then decelerates at a known deceleration (2m/s/s) to standstill. The total...
  24. N

    Finding the area of trapezoid area question

    (double integral) cos((y-x)/(y+x))dA Where the double integral is over the region with points (1, 0), (2, 0), (0, 2), and (0, 1). I think the trapezoid is enclosed by y+x = 1 y+x = 2 y=0 x=0 How can I use this? Thanks
  25. Q

    Trapezoid method using a loop

    dear users I want to do a triple integration over x ,y ,z in MATLAB but because my expression under the integral is so complicated I want to change integrals to sum by Trapezoid method using a loop in MATLAB but for doing that I have 3 integrals and so 3 for loops for summing over x , y , z...
  26. C

    Same Areas of Trapezoid within Triangle, why?

    Good day, while reading up on an elementary math study book, i have encountered that a proof is build upon the following (see attachment for the figure). Are the Areas CDE and BED really the same? I tried to calculate this from abstraction, not sure where I could have made a mistake.. g1 is the...
  27. D

    Trapezoid - Calculus of Several Variables

    First time posting on this forum so let's see how this goes! Homework Statement The base B of a trapezoid increases in length at the rate of 2cm/sec and the top T decreases in length at the rate of 1cm/sec. If the height h is increasing at the rate of 3cm/sec how rapidly is the area A...
  28. C

    MHB What is the maximum area of this isosceles trapezoid? - - - - (I created this problem.)

    Given: an isosceles trapezoid The shorter base is 8 units in length The slant height is 12 units in length.What is the maximum area that this isosceles trapezoid could have? You could answer with either an exact number, or an answer where the value is to the nearest hundredths of square...
  29. T

    Maximizing area of trapezoid Drain Gutter

    Homework Statement Image is very big. Angles A and B are 120° length of metal is 5m width of metal is 0.6m it's an isosceles trapezoid drainage. Homework Equations ° in a trapezoid: 180(n-2) A = 2(bh/2) + whThe Attempt at a Solution I'm not sure, I started but I'm not even sure if I'm...
  30. L

    Geometry - Can a trapezoid ever be a kite, and vice versa?

    Homework Statement Can a trapezoid ever be a kite? Can a kite be a trapezoid? 2. The attempt at a solution I believe that the answer to both is no. 1. If a trapezoid was a kite, wouldn't the pair of parallel sides, along with the congruent consecutive sides, imply that it was a...
  31. B

    Find the area of a trapezoid using integration

    Homework Statement Homework Equations The Attempt at a Solution I don't see why you have to put the ((x/2)+ 3)dx next to the equation for a trapezoid. I also don't understand what number would equal x, 4? 2?. Also, the dx, what equation am I supposed to be deriving? .5((B+b)/2)h? that...
  32. I

    Using Trapezoid Rule Twice huh?

    Homework Statement Homework Equations A=(1/2)w[E+2M] Where w=width between each interval E=f(a0)+f(an) is the sum of the end values M=f(a1)+f(a2)+...f(an-1) The Attempt at a Solution I found the area of the first trapezoidal rule but can't identify the other w=(15/5)=3metres...
  33. Femme_physics

    Trapezoid weird angle result

    Homework Statement http://img69.imageshack.us/img69/281/trap01.jpg [Broken] AC and AC both equal 13. The given angles are in the pic. The Attempt at a Solution Attached. Why do I get angle ADC 70? It doesn't make visual sense, and I was told by a very smart person to always trust my visual...
  34. G

    MATLAB Lotka-Volterra Approximate Solution Error: Trapezoid Method in Matlab

    I'm trying to calculate the error of the Trapezoid Method in my population approximations for wolves and moose over time given certain parameters. Ultimately what i need to do is perform a series of trapezoid approximations using different 'h' values. Each successive 'h' value I use is half...
  35. H

    Maximizing Area of Cross-Section of Isosceles Trapezoid

    Homework Statement attached. It is just part a i am attempting for now. Homework Equations area of trapezoid = h(b1+b2 / 2) where h is height, b1 is base one and b2 is base two. The Attempt at a Solution i really tried, i didn't know where to start. the answer i got was 30cm for base...
  36. R

    Two trig questions (Triangles and Trapezoid)

    Homework Statement An isosceles trapezoid has a height of 4 cm and bases 3 cm and 7 cm long. How long are its diagonals? From lighthouses P and Q, 16km apart, a disabled ship S is sighted. If angle SPQ = 44 and angle SQP = 66, find the distance from S to the nearer lighthouse? I...
  37. U

    Finding the trapezoid of smallest perimeter given a,b,h

    Hi all, It seems obvious that the trapezoid with the smallest perimeter given the lengths of the bases and the height is the isosceles trapezoid. How can I prove this (preferably using analytical methods)? Note: this is not homework or anything. I need to know this as a step to prove the...
  38. J

    Maximizing a Trapezoid

    Homework Statement A gutter is to be made from a long strip of sheet metal 24 cm wide, by bending up equal amounts at each side through equal angles. Find the angle and the dimensions that will make the carrying capacity of the gutter as large as possible.Homework Equations The Attempt at a...
  39. B

    Finding the Force Exerted on a Log Using Virtual Work Calculations

    Virtual work (fireplace thong) Homework Statement http://s2.photobucket.com/albums/y31/bambidurojay/?action=view&current=fireplacetong.jpg I have been given a fireplace thong and need to determine the force exerted on a log. Homework Equations It is in the virtual work chapter of my...
  40. rocomath

    Calculating Water Level Rise in Trapezoid Trough

    Homework Statement A water trough is 10m long and a cross-section has a shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has a height of 50cm. If the bottom of the trough is being filled with water at the rate of .2m^3/min, how fast is the water level...
  41. E

    Solving erf(1.00) with Trapezoid Rule (n=6)

    http://en.wikipedia.org/wiki/Error_function If you have erf(1.00) and are asked to solve for the approximate value by using the trapezoid rule with n=6, how would you go about doing so? Since the function is erf(x) the 'x' goes into the limits of integration but a 't' is used as a variable...
  42. Y

    Geometry: Area of Trapezoid Circumscribed About A Circle

    Hiii, this is a problem that I have encountered and I need help ASAP. This is the figure: http://img404.imageshack.us/img404/1120/mathhelpppp6yk.gif [Broken] Thanks a lot! P.S. I apologize for posting at wrong forum
  43. Y

    Find the area of trapezoid circumscribed about a circle?

    Hello, I have encounted this problem and really need some help =/ The figure is attached. Or you can view it in here: http://img404.imageshack.us/img404/1120/mathhelpppp6yk.gif" [Broken] Thanks a lot, really urgent :frown:
  44. C

    Is Mid(n) an Underestimate for Trapezoid Integration on an Increasing Function?

    For F(x) dx from a to b show TRAP(n)=Left(n) + 1/2 (f(b)-f(a))*delta x