A2. A large square is split into four congruent squares, two of which are shaded. The other two squares have smaller shaded squares drawn in them whose vertices are the midpoints of the sides of the unshaded squares.
What fraction of the large square is shaded?
SolUtion
The two larger grey squares make up $\frac{1}{2}$ of the large square. Each white square is $\frac{1}{4}$ of the large square and $\frac{1}{2}$ of each of these squares is shaded. Therefore, the two smaller grey squares account for $2 \times \frac{1}{2} \times \frac{1}{4}=\frac{1}{4}$ of the large square. Therefore, $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$ of the large square is shaded.