It is learned after students have mastered the names and characteristics of each part of trapezoid and the area calculation methods of rectangle, square, parallelogram and triangle, which is the basis for further learning the combined graphic area and other graphic areas.
Put two identical trapeziums together to form a parallelogram, and the area formula of the trapezium is deduced as follows.
The method of deducing trapezoidal area;
1, put two identical trapezoids into a parallelogram.
The height of parallelogram is the height of trapezoid, and the bottom of parallelogram is the upper bottom plus the lower bottom of trapezoid.
The area of a parallelogram is the base times the height, and the area of a trapezoid is half that of a parallelogram, so the area of a trapezoid = (upper base+lower base) × height ÷2.
2. Cut the upper trapezoid along the connecting line between the two waist midpoints of the trapezoid to form a parallelogram.
The base of the parallelogram is the upper base plus the lower base of the trapezoid, and the height of the parallelogram is half that of the trapezoid.
The area of parallelogram = bottom × height, so the area of trapezoid = (upper bottom+lower bottom) × height ÷2.
3. Cut out two small triangles along two vertical lines drawn from the midpoint of the waist to the bottom to form a rectangle.
The length of the rectangle is half of the sum of the top, bottom and bottom of the trapezoid, and the width of the rectangle is the height of the trapezoid.
The area of a rectangle is long by wide, and the length of the rectangle is half of the sum of the top and bottom of the trapezoid, so the area of the trapezoid = (top and bottom+bottom) × height ÷2.
4. Divide the trapezoid into two triangles along the diagonal of the trapezoid.
The area of one triangle = bottom x height ÷2, and the area of the other triangle = top and bottom x height ÷2.
The area of a trapezoid is the sum of two triangles. Therefore, the area of trapezoid = (upper bottom+lower bottom) × height ÷2.
The reason why this derivative method is finally divided by 2 is because the areas of both triangles are divided by 2, so the final trapezoidal area is also divided by 2 after using the multiplication and distribution law.