Although the preferred SI unit of area is the square meter,...

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to $10,000 \mathrm{~m}^{2}$. In the English system, land is often measured in acres ( 1 acre $=160$ rod $^{2}$ ). Use the exact conversions and those given in Exercise 43 to calculate the following. a. $1 \mathrm{ha}=$_____$\mathrm{km}^{2}$ b. The area of a $5.5$ -acre plot of land in hectares, square meters, and square kilometers c. A lot with dimensions $120 \mathrm{ft}$ by $75 \mathrm{ft}$ is to be sold for $\$ 6500$. What is the price per acre? What is the price per hectare?

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to $10,000 \mathrm{~m}^{2}$. In the English system, land is often measured in acres ( 1 acre $=160$ rod $^{2}$ ). Use the exact conversions and those given in Exercise 43 to calculate the following.
a. $1 \mathrm{ha}=$_____$\mathrm{km}^{2}$
b. The area of a $5.5$ -acre plot of land in hectares, square meters, and square kilometers
c. A lot with dimensions $120 \mathrm{ft}$ by $75 \mathrm{ft}$ is to be sold for $\$ 6500$. What is the price per acre? What is the price per hectare?

Key Concepts

Dimensional Analysis and Unit Conversion

Dimensional analysis is a fundamental technique used in converting between different units of measurement. It involves multiplying by conversion factors that relate different units, ensuring that the final value is expressed in the desired unit. This process is crucial when dealing with a mix of metric and imperial measurements, such as converting from acres to hectares or square meters to square kilometers.

Imperial Area Measurement

In the English system, area is often measured using units like acres and rods. One acre is defined as 160 rod², making it a distinctive unit in land measurement. Understanding and converting imperial units to metric units involves knowing their exact conversion factors, which is important for accurate and meaningful comparisons between systems.

SI Units of Area

SI units provide a standardized method for measuring quantities, and in the case of area, the base SI unit is the square meter (m²). This allows for consistency in measurement and ease in calculations across various problems involving area, regardless of the specific context or application.

Metric Area Conversion

In the metric system, common area units include the square meter, hectare, and square kilometer. A hectare is defined exactly as 10,000 m², and converting between these units involves multiplying or dividing by powers of ten. Such conversions are essential for comparing and understanding areas measured in different scales within the metric system.

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