15. Each square in the grid shown is $1 \mathrm{~cm}$ by $1 \mathrm{~cm}$. What is the area of the shaded figure, in $\mathrm{cm}^{2}$ ?
A 14
B 15
C 16
D 17
E 18
Solution
D

The area of the grid, in $\mathrm{cm}^{2}$, is $3 \times 9=27$. The unshaded region consists of four triangles. Therefore the area of the unshaded region, in $\mathrm{cm}^{2}$, is $\frac{1}{2} \times 2 \times 3+\frac{1}{2} \times 2 \times 1+\frac{1}{2} \times 3 \times 2+\frac{1}{2} \times 2 \times 3=3+1+3+3=10$.
Therefore the area of the shaded figure, in $\mathrm{cm}^{2}$, is $27-10=17$.