Convert ground area to same units

Convert ground area from $m^2$ to $cm^2$. Since $1 m = 100 cm$, then $1 m^2 = 100°2 cm^2 = 10,000 cm^2$. Thus, $6561 m^2 = 6561 \times 10,000 cm^2 = 65,610,000 cm^2$.

$6561 m^2 = 65610000 cm^2$

Apply R.F. formula

The Representative Fraction (R.F.) is the square root of the ratio of areas: $R.F. = \sqrt{\frac{\text{Area on map}}{\text{Area on ground}}}$.

$R.F. = \sqrt{\frac{81}{65610000}}$

Calculate the square root

Calculating the square root of both numerator and denominator: $\sqrt{81} = 9$ and $\sqrt{65610000} = 8100$.

$R.F. = \frac{9}{8100} = \frac{1}{900}$