21. Freda's flying club designed a flag of a flying dove on a square grid as shown.
The area of the dove is $192 \mathrm{~cm}^{2}$. All parts of the perimeter of the dove are either quarter-circles or straight lines. What are the dimensions of the flag?

A $6 \mathrm{~cm} \times 4 \mathrm{~cm}$
B $12 \mathrm{~cm} \times 8 \mathrm{~cm}$
C $21 \mathrm{~cm} \times 14 \mathrm{~cm}$

D $24 \mathrm{~cm} \times 16 \mathrm{~cm}$
E $27 \mathrm{~cm} \times 18 \mathrm{~cm}$
21. D Let each of the small squares in the grid have side-length $x \mathrm{~cm}$. Remove the shading and divide the dove into regions as shown.
It can be seen that the regions marked $\mathrm{A}$ and $\mathrm{B}$ combine to make a square of side $2 x \mathrm{~cm}$ and hence of area $4 x^{2} \mathrm{~cm}^{2}$. Similarly, regions C, D and E combine to make a rectangle with sides $2 x \mathrm{~cm}$ and $3 x \mathrm{~cm}$ and hence area $6 x^{2} \mathrm{~cm}^{2}$. Finally, region $\mathrm{F}$ is a rectangle with sides $2 x \mathrm{~cm}$ and $x \mathrm{~cm}$ and hence area $2 x^{2} \mathrm{~cm}^{2}$. Since the total area of the dove is $192 \mathrm{~cm}^{2}$, we have $4 x^{2}+6 x^{2}+2 x^{2}=192$ and hence $12 x^{2}=192$. Therefore $x^{2}=16$ and hence $x=4$. Hence the flag has length $(6 \times 4) \mathrm{cm}=24 \mathrm{~cm}$ and height $(4 \times 4) \mathrm{cm}=16 \mathrm{~cm}$.