8. In the diagram, the area of the large square is $16 \mathrm{~cm}^{2}$ and the area of each small corner square is $1 \mathrm{~cm}^{2}$. What is the shaded area?
A $3 \mathrm{~cm}^{2}$
B $\frac{7}{2} \mathrm{~cm}^{2}$
C $4 \mathrm{~cm}^{2}$
D $\frac{11}{2} \mathrm{~cm}^{2}$
E $6 \mathrm{~cm}^{2}$
SolUtion
C

Since the area of the large square is $16 \mathrm{~cm}^{2}$ and the area of each small square is $1 \mathrm{~cm}^{2}$, their side-lengths are $4 \mathrm{~cm}$ and $1 \mathrm{~cm}$ respectively. Therefore the base of each of the four triangles is $2 \mathrm{~cm}$ and, since these triangles meet at the centre of the large square, the height of each triangle is also $2 \mathrm{~cm}$. Therefore the total area of the four triangles is $\left(4 \times \frac{1}{2} \times 2 \times 2\right) \mathrm{cm}^{2}=8 \mathrm{~cm}^{2}$. Hence the shaded area is $(16-8-4 \times 1) \mathrm{cm}^{2}=4 \mathrm{~cm}^{2}$.