Question

The unit of land measure in the English system is the acre, while that in the metric system is the hectare. An acre is \(4.356 \times 10^{4} \mathrm{ft}^{2}\). A hectare is ten thousand square meters. \(\mathrm{A}\) town requires a minimum area of 2.0 acres of land for a single-family dwelling. How many hectares are required?

Short answer

Answer: Approximately 0.81 hectares.

Step-by-step solution

Understanding the Conversion Rates

To start, recall that 1 acre is \(4.356 \times 10^{4} \mathrm{ft}^{2}\) and 1 hectare is equivalent to ten thousand or \(1.0 \times 10^{4}\) square meters.

Converting Square Feet to Square Meters

To convert from one unit to another, we need a conversion factor. In this case, we know that 1 square foot is approximately equal to \(0.0929030\) square meters. Therefore, we can find the area in square meters of one acre by multiplying the given value of an acre, in square feet, by the conversion factor.

Calculation of One Acre in Square Meters

Knowing the conversion factor and the area of one acre in square feet, we can calculate the area of one acre in square meters: \[ \text{Area}_{\text{acre}} = 4.356 \times 10^{4} \mathrm{ft}^{2} \times 0.0929030 \mathrm{m}^{2}/\mathrm{ft}^{2} = 4046.86 \mathrm{m}^{2} \]

Conversion of Acres into Hectares

Since 1 hectare = \(1.0 \times 10^{4}\) square meters and we now have the area of one acre in the same unit, we can express one acre in terms of hectares. \[ \text{Area}_{\text{acre}} = \frac{4046.86 \mathrm{m}^{2}}{1.0 \times 10^{4} \mathrm{m}^{2}/ \mathrm{hectare}} = 0.404686 \mathrm{hectares} \]

Calculating the Required Area in Hectares

The last step is to multiply the area per acre in hectares that we just calculated by the required area in acres (2.0 acres). This will give us the equivalent area in hectares for the required land for a single-family dwelling. \[ \text{Required Area} = 2.0 \,\text{acres}\times 0.404686 \,\text{hectares/acre} = 0.809372 \,\text{hectares} \] So, about 0.81 hectares of land are required for a single-family dwelling.