Question

A map is drawn to a scale of 1:5000, if the actual area of the plot is 0.4km^2. Find the area of this plot on the map?

Answer 1

1.6\times 10^{-8}\ km^2

Explanation:

Let `L` & `L'` be the actual & reduced linear dimensions of the plot then the ratio of linear dimensions
`\frac{L'}{L}=\frac{1}{5000}`
But area of plot `A\propL^2`
Hence the ratio of reduced area `A'` & the actual area `A` will be as follows
`\frac{A'}{A}=\frac{L'^2}{L^2}=(\frac{ L'}{L})^2`
`A'=A(\frac{ L'}{L})^2`
`=0.4(\frac{1}{5000})^2`
`=1.6\times 10^{-8}\ km^2`