2. A large square of side-length $10 \mathrm{~cm}$ contains a smaller square of side-length $4 \mathrm{~cm}$, as shown in the diagram. The corresponding sides of the two squares are parallel. What percentage of the area of the large square is shaded?
A $25 \%$
B $30 \%$
C $40 \%$
D $42 \%$
E $45 \%$
SolUtion
D

The length of the big square is $10 \mathrm{~cm}$ and of the smaller is $4 \mathrm{~cm}$. The total height of the shaded regions is 6 . Hence the total area of the two trapezoids combined is $\frac{10+4}{2} \times 6=42 \mathrm{~cm}^{2}$. Since the total area is $100 \mathrm{~cm}^{2}$ this is $42 \%$.