16. Inside a square of area $36 \mathrm{~cm}^{2}$, there are shaded regions as shown. The total shaded area is $27 \mathrm{~cm}^{2}$. What is the value of $p+q+r+s$ ?
A $4 \mathrm{~cm}$
B $6 \mathrm{~cm}$
C $8 \mathrm{~cm}$
D $9 \mathrm{~cm}$
E $10 \mathrm{~cm}$
16. D Since the area of the square is $36 \mathrm{~cm}^{2}$, the length of a side of the square is $6 \mathrm{~cm}$. Since the shaded area is $27 \mathrm{~cm}^{2}$, the area not shaded is $(36-27) \mathrm{cm}^{2}=9 \mathrm{~cm}^{2}$. Let $a \mathrm{~cm}, b \mathrm{~cm}$ and $c \mathrm{~cm}$ be the lengths of the parts of the sides shown on the diagram. The area of a triangle is $\frac{1}{2} \times$ base $\times$ height.

Therefore $\frac{1}{2} \times a \times 6+\frac{1}{2} \times b \times 6+\frac{1}{2} \times c \times 6=9$ and hence $a+b+c=3$. Therefore, since $(a+b+c)+(p+q+r+s)$ is the sum of the lengths of two sides of the square and so is equal to $12 \mathrm{~cm}$, the value of $p+q+r+s$ is $9 \mathrm{~cm}$.