How to find the basis of the trapeze?

Before you start talking about how to findthe basis of the trapezoid, it is important to understand what a trapezoid is. A trapezoid is a geometric figure that is a quadrilateral with two parallel sides that oppose each other. These aspects in mathematics are called the bases of the trapezium. The other two sides are called the sides. If we connect the central points of the sides, we will obtain the middle line of the trapezoid. These properties of this geometric figure are the basis of all calculations of its characteristics.

To calculate the base of the trapezoid, as a large,both small and small, a number of methods are used. The choice of method depends on the amount of knowledge that we have about the object. Most tasks have conditions that contain data that significantly simplifies the search for a solution to the problem. Often, the solution is to lower the height to the ground, applying 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 is calculatedan isosceles trapezoid. An isosceles trapezoid is a trapezoid, which has equal lateral sides. The figure has a symmetrical view relative to the center, this makes the pairs of its angles equal. Thus, information about one corner simplifies the task of calculating all other angles.

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

How to find a smaller base of an isosceles trapezoid

In the case when we know the size of the larger base, the question of how to find a smaller base of an isosceles trapezium will cease to be acute. This can be done as follows:

1. On a larger base, the height should be lowered.
2. Write down two theorems of Pythagoras, one of whichwill reflect the parameters of the triangle, and the other will be needed for a triangle consisting of a 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 reach the height, and the other will have a larger base that does not have a segment. The segment will be cut off by height. The second theorem is used for a triangle, the components of which are the hypotenuse - the side and the cathete - a section of a large base limited by height.
3. Draw up a system of equations that have been obtained, solve them.
4. Find the segment cut off by the height from the largest distance.
5. Take the doubled 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 kind of geometricTrapezium, one of the angles of which is equal to ninety degrees. Calculate the base of the rectangular trapezium most easily. The condition of the problem, as usual, already contains data on the second basis. From you only need to determine the fragment of the base, which forms the angle of the figure along with the side.

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