How to find the base of the trapezoid?

Before you start talking about how to find the base of a trapezoid, it is important to understand what a trapezium is. A trapezoid is a geometric shape that is a quadrilateral with two parallel sides that are opposite to each other. These sides in mathematics are called trapezoid bases. The other two sides are called lateral sides. If we connect the central points of the sides, we get the center line of the trapezium. These properties of this geometric figure are the basis of all calculations of its characteristics.

To calculate the base of the trapezoid, both large and small, a number of methods are used. The choice of method depends on the amount of knowledge we have about the object. Most tasks have conditions that contain data that significantly simplifies the search for a solution to a problem. Often, the solution is to lower the height to the base, using the Pythagorean theorem, in this case it is easy to solve the problem.

How to find the base of an isosceles trapezium

Similarly, the base of an isosceles trapezoid is calculated. An equilateral trapezium is a trapezium that has equal sides. The figure has a symmetrical appearance relative to the center, this makes pairs of its angles equal. Thus, information about one angle simplifies the task of calculating all other angles.

The side parts of the trapezoid are equal to each other. For example, we must find a base through a fragment of this base. The length of the second fragment in this case will coincide with the length of the first fragment with absolute accuracy. We can also get the desired part of the base through the image of height, which forms a triangle. The parameters of the angles and one side of the triangle will help us make accurate calculations. In problems, it is necessary to solve the problem of how to find a larger base of an isosceles trapezium or a smaller base. Consider an example of calculating the magnitude of the smaller base of a trapezoid.

How to find the smaller base of an isosceles trapezium

In the case when we know the magnitude of the larger base, the question of how to find the smaller base of an isosceles trapezoid will cease to be acute. It can be as follows:

  1. On a larger basis, you need to lower the height.
  2. Write two Pythagorean theorems, one of which will reflect the parameters of the triangle, and the other will be needed for the triangle consisting of the hypotenuse. In the case of the first theorem, in the triangle the role of the hypotenuse will be fulfilled by the diagonal, the role of one leg will be given to the height, and the other - the larger base, which does not have a segment. The segment will be cut off by height. The second theorem is used for a triangle whose components will be the hypotenuse - the lateral side and the leg - a segment of a large base, limited by height.
  3. Create a system of equations that are obtained, solve them.
  4. Find the segment, cut off from the greatest distance.
  5. Subtract twice the parameters of the obtained segment from the parameters of the largest base.
  6. Get the result - the length of the smallest base.

How to find the base of a rectangular trapezoid

A rectangular trapezoid is a type of geometric trapezium, one of the corners of which is ninety degrees. Calculate the base of a rectangular trapezoid most easily. The condition of the problem, as usual, already contains data on the second basis.All you need to do is identify the fragment of the base that forms the angle of the figure along with the side.

By the Pythagorean theorem, we calculate this part, then we need to add or subtract this part from the second base. As a result of calculations, we obtain the desired parameter. Now you know how to find the base of a rectangular trapezoid.

Date: 09.10.2018, 10:22 / Views: 93542

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