Rectangular trapezoid and its properties

This geometric figure - a rectangular trapezoid - has not only a great mathematical, but also a physical distribution. After all, everything that is given in the school curriculum has a related application. So, for example, knowing what the area of a rectangular trapezoid is equal to, it is easy to find the path of the body with uniformly accelerated motion. How to do it? Now consider.

The area of a certain type of figure is calculated in different ways. In our case, it is necessary to know the sum of the two bases and the height. The last one is one of the sides, lying at the right angle. Total, the desired result is calculated as follows:

S = (a + b) * h / 2

Of course, this dependence is not taken from the ceiling. It is possible that someone knows about the midline, which contains both a conventional and a rectangular trapezoid. If it is denoted by the letter m, then the value can be found as follows: m = (a + b) / 2. Mentally, slide this segment down. It will be something like the length of a known rectangle. It is on the reduction to this simplest figure that the first reduced dependence is constructed. In general, the formula for the area of a rectangular trapezoid involves the possibility of replacing h (height) by the side length at an angle of 90 degrees. Some should immediately understand that this is justified by the equality between these quantities.

In the beginning, we have already mentioned the possibility of applying the values of a figure in physics. In particular, the principle of uniformly accelerated motion should be well known to schoolchildren. A rectangular trapezoid is the case where the initial velocity is zero, the acceleration is constant. If the task posed requires you to calculate the path taken in this situation, then you can use the formula to find the area. Variable "a" let it denote the whole time of the path. We should say right away that we are working in a Cartesian coordinate system. Then "b" will denote the time during which the maximum speed was. Accordingly, if, up to the end of the motion, it remained uniformly accelerated, then b = 0. For h we take the value of steady speed. After substituting the values, you get the path, since it can be calculated by the formula S = V average * t. Now you know how a rectangular trapezoid can help you.

To solve problems one should know only a few formulas for the figure in question. For example, the sum of the angles at the inclined side is 180 degrees. The diagonal relative to one of the sides is the hypotenuse of a right-angled triangle with known legs. Remember that far from any quadrilateral, especially in a rectangular trapezoid, you can enter a circle. There are many definitions in the school course, but the main thing is to be extracted from them. For example, the fact that a rectangular trapezoid has all the properties of a normal trapezoid, but also has some additional features. Suppose that the base is four, the side is three, and the diagonal that connects them is 5. By the Pythagorean theorem, 3 * 3 + 4 * 4 = 5 * 5. From this it follows that we have a rectangular trapezoid.

So, you met one more geometric figure. The formula for finding its area does not need to be learned, it is enough to understand the principle of calculation.