Which of the following is a unit of area? A) Meter per second squared, B) centimeter, C) cubic meter, D) square meter.
We know that an area involves units of length times length, or length squared. As we evaluate our options then, we’ll look for this length-squared value. Considering option A, meters per second squared, the dimensions of that term is a length times a time to the negative two. Since we’re looking for a length times a length, or a length squared, we know that A is not a unit of area.
Next, we consider the centimeter. The centimeter is itself a length. But again, since we’re looking for length squared, length to the first power isn’t an area. Moving on to consider a cubic meter, the dimensions of a cubic meter are length times length times length, or length cubed. This is close, but we want length squared. So this means that a cubic meter is not a unit of area.
Finally, we consider the square meter. A square meter has dimensions of length times length, or length squared. As we compare this with our diagram, we see that this will indeed give us an area. This means that option D, the square meter, is a unit of area.