10. The diagram shows two arrows drawn on separate $4 \mathrm{~cm} \times 4 \mathrm{~cm}$ grids. One arrow points North and the other points West.
When the two arrows are drawn on the same $4 \mathrm{~cm} \times 4 \mathrm{~cm}$ grid (still pointing North and West) they overlap. What is the area of overlap?

A $4 \mathrm{~cm}^{2}$
B $4 \frac{1}{2} \mathrm{~cm}^{2}$
C $5 \mathrm{~cm}^{2}$
D $5 \frac{1}{2} \mathrm{~cm}^{2}$
E $6 \mathrm{~cm}^{2}$
Solution: $\mathbf{E}$
By drawing one arrow on top of the other, as shown, we see that the region of overlap covers the whole of 4 of the $1 \mathrm{~cm} \times 1 \mathrm{~cm}$ squares into which the grid is divided, and 4 halves of these squares. So the area of the overlapping region is $4+4\left(\frac{1}{2}\right)=6 \mathrm{~cm}^{2}$.