8. In the diagram, the centre of the top square is directly above the common edge of the lower two squares. Each square has sides of length $1 \mathrm{~cm}$. What is the area of the shaded region?
A $\frac{3}{4} \mathrm{~cm}^{2}$
B $\frac{7}{8} \mathrm{~cm}^{2}$
C $1 \mathrm{~cm}^{2}$
D $1 \frac{1}{4} \mathrm{~cm}^{2}$
E $1 \frac{1}{2} \mathrm{~cm}^{2}$
8. C The centre of the top square is directly above the common edge of the lower two squares. Hence a rectangle half the size of the square, and so of area $\frac{1}{2} \mathrm{~cm}^{2}$, can be added to the diagram to form a right-angled triangle as shown. The area of the shaded region and the added rectangle is equal to $\left(\frac{1}{2} \times 2 \times 1 \frac{1}{2}\right) \mathrm{cm}^{2}=1 \frac{1}{2} \mathrm{~cm}^{2}$. Hence the area of the shaded region, in $\mathrm{cm}^{2}$, is $1 \frac{1}{2}-\frac{1}{2}=1$.