VTMO 2014 — Grade 8 — semifinal Question 10

Question 10

Square $1$ has area $64 \,\mathrm{cm}^{2}$. Each next square has diagonal equal to the preceding side, as shown. Find square $9$ area.

Question illustration

$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{1}{9}$