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.

Answer 1

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.