23. The diagram shows four shaded glass squares, with areas $1 \mathrm{~cm}^{2}, 4 \mathrm{~cm}^{2}$, $9 \mathrm{~cm}^{2}$ and $16 \mathrm{~cm}^{2}$, placed in the corners of a rectangle. The largest square overlaps two others. The area of the region inside the rectangle but not covered by any square (shown unshaded) is $1.5 \mathrm{~cm}^{2}$.
What is the area of the region where squares overlap (shown dark grey)?
A $2.5 \mathrm{~cm}^{2}$
B $3 \mathrm{~cm}^{2}$
C $3.5 \mathrm{~cm}^{2}$
D $4 \mathrm{~cm}^{2}$
E $4.5 \mathrm{~cm}^{2}$
23. D The diagram shows some of the lengths of sides which may be deduced from the information given in the question. Note that the rectangle measures $5 \mathrm{~cm}$ by $5.5 \mathrm{~cm}$. The sum of the areas of the four glass squares is $(1+4+9+16) \mathrm{cm}^{2}=30 \mathrm{~cm}^{2}$. However, the total region of the rectangle occupied by the four squares is equal to $(5 \times 5.5-1.5) \mathrm{cm}^{2}=26 \mathrm{~cm}^{2}$. So the area of the overlap is $(30-26) \mathrm{cm}^{2}=4 \mathrm{~cm}^{2}$.