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Question
A plot of land of area 20km2 is represented on the map with a scale factor of 1:200000. Find: The ground area in km2 that is represented by 2cm2 on the map.
Solution
1cm on the map = 200,000cm on the land (as the scale is 1:200000)
1cm2 on the map = (200000)2 on the land
1km = 100000cm
⇒ 1km2 = 100000 x 100000cm2
`"distance(map)"/"distance(land)"` = Scale
`(2)/("distance(land)" xx (100000)) = (1)/((200000)^2`
Hence 2cm on map
= `(2 xx 200000 xx 200000)/(100000 xx 100000)`
= 8km2.
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