RF and scale for 6.304 ha plot

RF

Ground area $= 6.304$ ha $= 6.304 \times 10^{4}$ m$^2 = 6.304 \times 10^{8}$ cm$^2$. Map area $= 4.7 \times 4.6 = 21.62$ cm$^2$.

$$\text{RF}^2 = \frac{21.62}{6.304 \times 10^{8}} = 3.4296 \times 10^{-8}$$ $$\text{RF} = 1.852 \times 10^{-4} \approx \frac{1}{5400}$$

Scale length (to read 1 m, up to 500 m)

$$\frac{500 \times 100}{5400} = 9.26\ \text{cm}$$

100 m $= 1.852$ cm, 10 m $= 0.1852$ cm, 1 m $= 0.01852$ cm.

Construction (diagonal scale)

1. Draw a line 9.26 cm long and divide it into 5 main divisions of 1.852 cm (100 m each), numbered 0, 100, ... 500. Extend one more division of 1.852 cm to the left of 0.
2. Divide this left division into 10 parts (10 m each, 0.1852 cm).
3. Draw 10 horizontal lines at equal spacing and the diagonals from the top of each sub-division to the next lower sub-division on the base. Each step along a diagonal reads 1 m.

Indicating 123.400 m

$123.4 = 100 + 20 + 3 + 0.4$. Take the vertical at 100 and the diagonal from the 20 sub-division. On this diagonal, mark a point 0.4 of the way from the 3rd to the 4th horizontal line (estimated by eye, since 0.4 m is only about 0.007 cm on the map). The horizontal distance from this point to the vertical at 100 represents 123.4 m.

 10 |  /  /  /  /  /  /  /  /  /  /  |
  3 |  .. 123.4 m                     |
  0 +---+---+---+---+---+---+---------+
   90..0  100  200  300  400  500 (m)

Answer: RF = 1/5400; scale length = 9.26 cm (plus the left sub-divided part).