21. The diagram shows a pentagon drawn on a square grid. All vertices of the pentagon and triangle are grid points.
What fraction of the area of the pentagon is shaded?
A $\frac{2}{7}$
B $\frac{1}{3}$
C $\frac{2}{5}$
D $\frac{1}{4}$
E $\frac{2}{9}$
21. A The area of the shaded triangle is $\frac{1}{2} \times 3 \times 6=9$. The area of the square grid is $6 \times 6=36$, and the area of the triangle which is not part of the area of the pentagon is $\frac{1}{2} \times 3 \times 3=\frac{9}{2}$. So the area of the pentagon is $36-\frac{9}{2}=\frac{63}{2}$. Hence the required fraction is $9 \div \frac{63}{2}=9 \times \frac{2}{63}=\frac{2}{7}$.