Question

On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD is measured as AB= 12 cm and BC = 16cm. calculate the diagonal distance of the plot in km and the plot area in km² . 

Answer 1

Scale :- 1 : 25000

1 cm represents 25000 cm = `25000/(1000 xx 100) = 0.25` km

1 cm represents 0.25 km

AC² = AB² + BC²

= 12² + 16²

= 144 + 256

AC²  = 400

AC = 20 cm

Actual length of diagonal = 20 × 0.25 = 5.00 = 5 km

1 cm represents 0.25 km

1 cm² represents 0.25 × 0.25 km²

The area of the rectanggle ABCD =  AB × BC

= 16 × 12 = 192 cm²

The area of the plot = 0.25 × 0.25 × 192 km² = 12 km²