The side of the frustum is developed into a sector ring, and the sector ring and the trapezoid share an area formula: (upper bottom+lower bottom) * height /2. Here, the upper and lower bottoms are perimeters 2π r and 2πr' respectively, and the height is bus L, so the area formula π(r'L+rl) is obtained.

Specifically, the area comparison formulas of triangle and sector are the same (base * height /2), trapezoid is the difference between two triangles and sector ring is also the difference between two sectors, so it can be deduced that the area formulas of sector ring and trapezoid are the same.