Area of a trapezoid half the product of the height and the sum of the lengths of the parallel sides

Area of the trapezoid is the sum of the area of the rectangle and the right triangles that are next to it.
Area of the trapezoid= l*h + h*x/2+h*[L-l-x)]/2=l*h+h*x/2+h*L/2-h*l/2-h*x/2=
                                  = h*L/2+h*l-h*l/2=h*L/2+h*l/2=h*(L+l)/2