Question

A building site measures 96 sq.cm on a scale of 1:12500. The actual area it represents (in hectare, in integer) is \(\underline{\hspace{1cm}}\).

Hint:

For area scaling, always square the scale ratio. Length scales linearly, but area scales with the square of the scale.

Answer 1

Correct Answer: 150

Given scale: \[ 1 : 12500 \] This means 1 cm on the map represents 12,500 cm in reality. Since this is an area problem, the scale factor must be squared: \[ (\text{Actual area}) = (\text{Map area}) \times (12500)^2 \] Map area: \[ A_{\text{map}} = 96\ \text{cm}^2 \] So, \[ A_{\text{actual}} = 96 \times 12500^2 \] \[ 12500^2 = 156{,}250{,}000 \] \[ A_{\text{actual}} = 96 \times 156{,}250{,}000 = 15{,}000{,}000{,}000\ \text{cm}^2 \] Convert to square meters: \[ 1\ \text{m}^2 = 10,000\ \text{cm}^2 \] \[ A_{\text{actual}} = \frac{15{,}000{,}000{,}000}{10,000} = 1{,}500{,}000\ \text{m}^2 \] Convert to hectares: \[ 1\ \text{hectare} = 10{,}000\ \text{m}^2 \] \[ A_{\text{actual}} = \frac{1{,}500{,}000}{10{,}000} = 150\ \text{hectares} \] Thus, the required actual area is: \[ \boxed{150} \]