A square drawing has an area of 4 cm square. If the scale of the drawing is 1 : 2 what is the area of the object

Scale 1:2 means that 1 cm on the drawing is 2 cm in reality. So the square is 8cm x 8cm = 64cm².

Notice that while the size gets two times as big, the area gets 2²=4 times as big. That can be confusing. If you actually draw the square on 1:1 and also on 1:2, you can easily see that the latter fits 4 times in the real size ...