Area is a derived quantity because it is defined as the amount of space occupied by a two-dimensional object. It is derived from the fundamental quantity of length. To calculate the area of a rectangle, for example, we need to multiply its length by its width. Both length and width are fundamental quantities, so area is a derived quantity.

Speed is also a derived quantity because it is defined as the rate of change of position. It is derived from the fundamental quantities of length and time. To calculate the speed of an object, for example, we need to divide the distance it travels by the time it takes to travel that distance. Both distance and time are fundamental quantities, so speed is a derived quantity.