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 = 16 cm. Calculate the diagonal distance of the plot in km and the plot area in km². 

On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD, has the following measurements: AB = 12 cm and BC = 16 cm. Angles A, B, C and D are 90° each. Calculate:

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

Answer 1

Scale:- 1 : 25000

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

1 cm represents 0.25 km

(i)

AC² = AB² + BC²

= 12² + 16²

= 144 + 256

AC²  = 400

AC = 20 cm

Actual length of diagonal = 20 × 0.25

= 5.00

= 5 km

Hence, the distance of a diagonal of the plot in km is 5 km.

(ii)

1 cm represents 0.25 km,

1 cm² represents 0.25 × 0.25 km²

The area of the rectangle ABCD =  AB × BC

= 16 × 12

= 192 cm²

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

Hence, the area of the plot in sq. km = 12 km²