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How to find the perimeter of a trapezoid

How to find the perimeter of a trapezoid

Trapezoid is a quadrangle with two parallel and two non-parallel sides. To calculate its perimeter, you need to know the size of all sides of the trapezoid.

The data can be in different tasks.

You will need

  • - kalkulyator-
  • - Tables of sines, cosines and tangensov-
  • - bumaga-
  • - Drawing equipment.



The simplest version of the problem - where are allside of the trapezoid. In this case, they should just fold. You can use the following formula: p = a + b + c + d, where p - perimeter, and letters a, b, c and d denote side opposite corners designated corresponding capital letters.


It is given isosceles trapezoid enoughput two of its foundation and add to it twice the size of the part. That is, in this case, the perimeter is calculated by the formula: p = a + c + 2b, where b - the trapezoid, and with - a base.


Calculations will be somewhat longer ifsome of the parties have to be calculated. For example, the known length of the base, adjacent to it angles and height. You need to calculate the short base and side. To do this, draw a trapezoid ABCD, from the top angle B draw BE height. You will get a triangle ABE. You know the angle A, respectively, you know his sinus. BE also the height specified in the data of the problem, which is also the legs of a right triangle opposite the well-known corner of you. To find the hypotenuse AB which is also the side of the trapezoid, enough BE divided into sinA. Similarly, the second party get the length. It needs to hold a different height from the upper corner, that is CF.
Now you know more bottom and sides. To calculate this small perimeter, we need more size smaller base. Accordingly, the two formed inside the trapezoid triangles need to find the dimensions of AE and DF segments. This can be done, for example, the cosine famous angles A and D. The cosine - is the ratio of the adjacent leg to the hypotenuse. To find a leg, you need to multiply by the cosine of the hypotenuse. Next calculate the perimeter of the same formula as in the first step, that is folded all sides.


Another option: Given two bases, and the height of one of the parties, it is necessary to find the other side. It is also better to make use of trigonometric functions. To do this, draw a trapezoid. Let's say you know the base AD and BC, as well as the side AB and BF height. From these data, you can find the angle A (via sine, that is the ratio of the height to the known side) AF segment (via a cosine or tangent, since the angle you already know Recall also the properties of the trapezoid corners -. The sum of the angles adjacent to one side of 180 °.
Spend height CF. You get another right-angled triangle in which you need to find the hypotenuse and the CD leg of the DF. Start with the leg. Subtract the length of the lower base of the upper length, and from the result - already known to you the length of the segment AF. Now, in a right triangle CFD you know the two leg, that is, you can find the tangent of an angle D, and on it - and the angle itself. Thereafter it remains the same through the sine of the angle calculated direction CD, as already described above.

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