Trapezoidal area formula Say how to count, and say the meaning, why

Trapezoidal area formula Say how to count, and say the meaning, why

From the two top points of the bottom to make the vertical line of the bottom, it is a rectangle and two right triangles, which should be proved here

Why fan ring and trapezoid share the same area formula? Can it be proved?

The fan ring formula is deduced as follows
Let the radius of the circle where the two arcs are located be r and R respectively (r > R), and the circumference angle be n, then the height is (R-R)
Then the area of one sector S1 = n / 360 * π * (R ^ 2) and the area of the other sector S2 = n / 360 * π * (R ^ 2), so the area of the sector ring s = S1-S2 = n / 360 * π * (R ^ 2-r ^ 2) = n / 360 * π (R + R) (R-R) = 1 / 2 * (n / 360 * 2 π R + n / 360 * 2 π R) (R-R), where n / 360 * 2 π R is the length of the long arc, equivalent to the upper bottom of the trapezoid; n / 360 * 2 π R is the length of the short arc, equivalent to the lower bottom of the trapezoid; and R-R is equivalent to the height
So share the same area formula