In Wikipedia there is a page of a trapezoid. In the drawing it is shown that any trapezoid can be turned into a rectangle.
![Trapezoid Trapezoid. Mathematics For Blondes.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF-NpWKqODcWftioQ5c1GJEUg4W1I_ItjI84ODcuXockRmbMJNZrnQmDUANiiZv67yiIbwpr_An-sWqXs8vcz4EQM-kM2g9E_4kLS6BaIqIDrHsnNR5OHPX7QjChlAhNywMCKMVfZFZZiM/s400/Trapezoid.jpg) |
Trapezoid |
Let's look at algebra. These are formulas for calculation of lengths of diagonals of a trapezoid.
![Diagonals of trapezoid Diagonals of trapezoid. Mathematics For Blondes.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivg68m-_lyQCCiavoRTz412TZ4cqVO39hA8LCPhmYY2ns3-dXT4w-TWp9YEV7V7KUdxLlopgs89wwqStp85GNEGR72f65hsKR2cP_09XkqJ7t1FB0vhlanAcVzTR4bfO_K0K6_iVODGslI/s400/Diagonals+of+trapezoid.jpg) |
Diagonals of trapezoid |
We substitute in these formulas data for a rectangle.
![Diagonals of rectangle Diagonals of rectangle. Mathematics For Blondes.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBp0G28xLT7lq5qh4uepjbbsiilcrOqBOXqSf0zkpuXeTM6RJ5NzPfk0wHJZI81n8Iv0ztJbnFXIPYD5myUxI5FaF5dyoV0G9oQhnqpbjGJ6jhM1V5ZxNByuVw0PryCTOPAxhTUzpfPo-d/s400/Diagonals+of+rectangle.jpg) |
Diagonals of rectangle |
If to trust these formulas, the rectangle has no diagonals. Even schoolboys or schoolgirls can make what mathematicians couldn't make – to execute verification of the solution of a task. It is the actual level of modern mathematics – any statement of mathematicians can be false.
Height of a trapezoid
Height of a trapezoid is determined by the area of a triangle. The area of a triangle is calculated on Heron's formula. The sizes of the parties of a trapezoid allow to receive a triangle which has the same height as a trapezjid. The cunning trick of mathematicians allows to calculate length of diagonals of a trapezoid.
![Height of a trapezoid Height of a trapezoid. Mathematics For Blondes.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxfrwcRiUFIxOfre31nRMxvOhepwdacTuNHCazlemWIi22yUO2BRbAj-T82TWy4TX0mn7VWk3xJCQSSdEjCvJRb_CdxgHADGnCDJFxlvNh5PwiJkVO3A9UJ3E1UiyQ7PuNnu9BYReV8Nub/s400/Height+of+a+trapezoid.jpg) |
Height of a trapezoid |
When the legs of a trapezoid are parallel, the triangle disappears and the cunning trick ceases to work. If to determine height of a trapezoid by the area of a trapezoid, then no problems arise upon transition to a rectangle or a parallelogram.
![Height of a rectangle Height of a rectangle. Mathematics For Blondes.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijqB3AG_a4NZISRujN1n4Y10jYcdNkj2vsfCJGfaXwRkAaXX_A7hO4NiO0eHzClQvIPmWjYj_ZXChTVjQL2TRgUJ9riCko2hVIH4u36dse_RJ6sv_sjMfPVzI1buezMO8aTAsQ61a_vU8O/s400/Height+of+a+rectangle.jpg) |
Height of a rectangle |
Conclusion: cunning tricks of mathematicians can lead in false results.