Question

On a map drawn to a scale of 1 : 25000, a triangular plot of a land is marked as ABC with AB= 6cm, BC = 8cm and ∠ ABC = 90° . Calculate the actual length of AB in km and the actual area of the plot in km² . 

Answer 1

Scale : -  : 1 : 25000

∴ 1 cm represents 25000 cm = `25000/(1000 xx 100) = 2.5` km

∴ 1 cm represents 0.25 km

Actual length of AB = 6 × 0.25 = 1.50 km

Area of Δ ABC = `1/2 xx "BC" xx "AB"`

`= 1/2 xx 8 xx 6 = 24  "cm"^2`

1 cm represents 0.25 km

1 cm² represents 0.25 × 0.25 km²

The area of plot = 0.25 × 0.25 × 25 km²

= .0625 × 24

= 1.5 km²