Scale of plan

On the plan of the village in the scale of 1: 1000 a rectangular garden is drawn. Its dimensions on the plan are 25mm and 28mm. Determine the area of the garden in ares.

Correct result:

S =  7 a

Solution:

$$\begin{gathered} a=25\text{ mm}\to \text{ m}=25\mathrm{/}1000\text{ m}=0.025\text{ m } \\ b=28\text{ mm}\to \text{ m}=28\mathrm{/}1000\text{ m}=0.028\text{ m } \\ {a}_1=1000\cdot a=1000\cdot 0.025=25\text{ m } \\ {b}_1=1000\cdot b=1000\cdot 0.028=28\text{ m } \\ {S}_1=a_1\cdot b_1=25\cdot 28=700{\text{m}}^2 \\ S=S_1\to \text{ a}=S_1\mathrm{/}100\text{ a}=700\mathrm{/}100\text{ a}=7\text{ a} \end{gathered}$$

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