Question

On a map, drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has AB = 24 cm and BC = 32 cm. Calculate : 

1. the diagonal distance of the plot in kilometer.
2. the area of the plot in sq. km.

Answer 1

Scale :- 1 : 20000

1 cm represents 20000 cm =`20000/(1000 xx 100) = 0.2  km`

i. AC² = AB² + BC²

= 24² + 32²

= 576 + 1024

= 1600

AC = 40 cm

Actual length of diagonal = 40 × 0.2 km = 8 km

ii. 1 cm represents 0.2 km

1 cm² represents  0.2 × 0.2 km²

The area of the rectangle ABCD = AB × BC

= 24 × 32

= 768 cm²

Actual area of the plot = 0.2 × 0.2 × 768 km² = 30.72 km²