Help Please!

We first focus on the second part of the statement. We find that $(1/2 \text{cm})^2 = \frac{1}{4} \text{cm}^2. $ Therefore, we get that $\frac{\frac{1}{4} \text{cm}^2}{\frac{1}{2} \text{cm}^2} = \boxed{\frac{1}{2}}.$

I agree with Cal.

They can certainly be interpreted as different but I would want the difference to be made more clear than this!

I think what they mean is:

the first one means cut a 1 cm square in half.    (It will be a rectangle with sides 0.5cm and  1cm)

The second one probably refers to a square with a side length of 0.5cm

  I agree this is very unclearly written....but I agree with BB...

    here is my interpretation:

   the entire figure below is   1/2 square centimeters   ( 1/2 cm²)

        the shaded area is   1/2 centimeters square   ....and is obviously   1/2   of the   1/2 cm²         ~ EP