On a map drawn to a scale of 1:50,000, a rectangular plot of land ABCD has the following dimensions

Mensuration (10)

On a map drawn to a scale of 1:50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles.

Find:

1. the actual length of the diagonal distance AC of the plot in km.
2. the actual area of the plot in square km.

Answer

$$AB = 6, BC = 8, Diagonal AC = \sqrt{6^2 + 82} = 10$$
$$i. \frac{10×50000} {1000} = 5 𝑘m$$
$$ii. \frac{6×8×50000×50000} {(100000^2)} = 12 sq  km$$