You can do it only of the triangle is right angled and if one of its legs is the same length as the side of the square. In that case, let that side of the triangle abut a side of the square.
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..._________________ ...\............/................../ ....\........../................../ .....\......../................../ ......\....../................../ .......\..../................../ ........\../................../ .........\/_________/ .........^triangle...^ ..........................^rhombus/parallelogram made from one trapezoid.
A triangle cannot be formed by any number of trapezoids. Every time a trapezoid is stretched across one side of a triangle, a smaller triangle similar to the first is formed by the part not covered by the trapezoid. Unless... the triangle was equilateral and the trapezoids were isoceles. You could fill the triangle with 3 trapezoids as follows: Use the longer 'bottom' edge of each trapezoid and the 'left' edge of the next trapezoid to make up the edge of the triangle. The shorter 'top' edge of the trapezoids touch the 'right' edge of the next trapezoid in the center of the triangle.
Place the two large triangles next to each other so that their hypotenuses together make the long parallel side of the trapezoid. Place the medium triangle between the two large triangles with its hypotenuse along the edge of one of the large triangles. Place one of the small triangles between the medium triangle and the other large triangle with its hypotenuse along the edge of the medium triangle Place the square between the large triangle and the small triangle so that its edges are along side the small triangle and the large triangle. Finally place the parallelogram between the square and the medium triangle (toughing both) to finish the isosceles trapezoid. The seventh piece,. the final small triangle, which is not used, can be placed on top of the parallelogram (with its hypotenuse touching) to create a large triangle,. An Isosceles trapezoid can also be formed from all 7 pieces - take the large square formed by all the pieces except the two large triangles (as above if the large triangle is completed), and put the two large triangles on opposite sides to complete the isosceles trapezoid.
No a square is not a trapezoid
You have to cut the trapezoid into three shapes. The three shapes will be two triangles and one rectangle or square. You have to find the area of these three shapes and then add all of the three areas up to find the area of the trapezoid.