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RF and scale for 0.55 hectare plot

Short answer

RF = 1/3000. A diagonal scale 13.33 cm long represents 400 m and reads single metres.

A rectangular plot of land of area 0.55 hectare is represented on a map of similar rectangle area of 6.11 cm². Calculate the representative factor of the scale of the map. Draw a scale to read upto a meter from the map. The scale should be long enough to measure upto 400 m.

RF

Ground area =0.55= 0.55 ha =5500= 5500 m2=5500×104^2 = 5500 \times 10^{4} cm2=5.5×107^2 = 5.5 \times 10^{7} cm2^2. Map area =6.11= 6.11 cm2^2.

RF2=6.115.5×107=1.1109×10−7\text{RF}^2 = \frac{6.11}{5.5 \times 10^{7}} = 1.1109 \times 10^{-7} RF=3.3331×10−4≈13000\text{RF} = 3.3331 \times 10^{-4} \approx \frac{1}{3000}

Scale (to read 1 m, up to 400 m)

Length=400×1003000=13.33 cm\text{Length} = \frac{400 \times 100}{3000} = 13.33\ \text{cm}

100 m =3.333= 3.333 cm, 10 m =0.3333= 0.3333 cm, 1 m =0.0333= 0.0333 cm: a diagonal scale.

Construction

  1. Draw a 13.33 cm line with 4 main divisions of 3.333 cm (100 m). Add one division to the left of 0.
  2. Divide the left division into 10 parts (10 m each).
  3. Draw 10 equally spaced horizontal lines on a rectangle 3 cm high.
  4. Draw the diagonals from the top of each sub-division to the next lower sub-division on the base. Each diagonal step gives 1 m.
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+----+----+----+--------------+
   90..0  100  200  300  400 (m)

Answer: RF = 1/3000; scale length = 13.33 cm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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