23. A square piece of paper of area $64 \mathrm{~cm}^{2}$ is folded twice, as shown in the diagram. What is the sum of the areas of the two shaded rectangles?

A $10 \mathrm{~cm}^{2}$
B $14 \mathrm{~cm}^{2}$
C $15 \mathrm{~cm}^{2}$
D $16 \mathrm{~cm}^{2}$
E $24 \mathrm{~cm}^{2}$
Solution
D

Consider the square divided up into 16 congruent smaller squares, as shown. Since the original square has area $64 \mathrm{~cm}^{2}$, each of the smaller squares has area $4 \mathrm{~cm}^{2}$. When the square is folded twice in the manner shown, it can be seen that each of the shaded rectangles is made up of two small squares. Therefore the sum of the areas of the two shaded rectangles is $2 \times 2 \times 4 \mathrm{~cm}^{2}=16 \mathrm{~cm}^{2}$.