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Scale for 39672 m² plan

Short answer

RF is 1/4000. A diagonal scale 10 cm long reads 1 m up to 400 m; use four 100 m divisions of 2.5 cm plus one left subdivision for 10 m. Diagonals give 1 m steps.

A plan represents an area of 39672 m² and represents 4.75 cm × 5.22 cm on plan. Find the scale of the plot and indicate through a sketch how a suitable scale can be constructed to read up to 1 m on the plan. The scale should be long enough to measure upto 400 m.

RF

Map area =4.75×5.22=24.795= 4.75 \times 5.22 = 24.795 cm2^2. Ground area =39672×104=3.9672×108= 39672 \times 10^{4} = 3.9672 \times 10^{8} cm2^2.

RF2=24.7953.9672×108=6.25×10−8,RF=2.5×10−4=14000\text{RF}^2 = \frac{24.795}{3.9672 \times 10^{8}} = 6.25 \times 10^{-8}, \qquad \text{RF} = 2.5 \times 10^{-4} = \frac{1}{4000}

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

Length=400×1004000=10 cm\text{Length} = \frac{400 \times 100}{4000} = 10\ \text{cm}

100 m =2.5= 2.5 cm, 10 m =0.25= 0.25 cm, 1 m =0.025= 0.025 cm. This is a diagonal scale.

Sketch and construction

  1. Draw a 10 cm line divided into 4 main divisions of 2.5 cm (100 m each); add one division to the left of 0.
  2. Divide the left division into 10 parts of 0.25 cm (10 m).
  3. Draw 10 horizontal lines (height 2.5 cm) and the diagonals from the top of each sub-division to the next lower sub-division at the base.
  4. Each step along a diagonal = 1 m.
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+----+----+----+----+--------+
   90..0  100  200  300  400 (m)

Answer: RF = 1/4000; scale length = 10 cm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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