10.6.7 Estimating Areas

A hectare (abbreviation: ha) is defined as the area of a square 100 m by 100 m. Therefore, one times ha equals 10,000 m super two. Alternatively, since 100 m equals zero .1 km, a hectare is the same as 0.01 times km super two.

The relationships between these different areas (km2, ha, m2, cm2, mm2) can be summarized by using a diagram similar to those we used in Unit 5.

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For example, suppose an area of lawn marked on a garden plan is approximately rectangular and measures 2 cm by 3.5 cm. If the scale of the map is 1:200, what is the actual area of the lawn?

If the scale is 1:200, the lengths on the ground will be 200 times the lengths on the plan. [ Why is it not usually possible to estimate large areas (e.g., the area of a country) from, say, a world map? ]

So, the width of the lawn = two multiplication 200 cm equals 400 cm equals four m.

The length of the lawn = 3.5 multiplication 200 cm equals 700 cm equals seven m.

That means the area of the lawn equals four m prefix multiplication of seven m equals 28 m super two.

Notice that you would have obtained the same answer by keeping the lengths in centimeters, calculating the area in cm super two and then converting to m super two.

Area of the lawn equals 400 cm prefix multiplication of 700 cm equals 280,000 cm super two.

To convert this area to m super two, divide by the conversion factor of 10,000, so area of lawn equals 280 comma 000 m super two division 10 comma 000 equals 28 times m super two, as before.

It is usually easier to convert as early as possible in a calculation—compare the conversion required using the first method here and the second method.

[ An acre was originally defined as the area that could be plowed in a day by a yoke of oxen. It is 4,840 square yards. ] The US or imperial measure of large area is the acre. If you look at advertisements for houses, you may find that some properties have information about the size of the lot or garden. Normally these are in terms of acres with gardens being described as one divided by four acre, 1 acre, or 3 acres. But how large are these areas?

It sometimes helps to compare a new measurement with something you can visualize. For example, a standard adult soccer field is approximately 1.5 acres. So if you want to set up a soccer field in your garden, you now know how much space you need! An acre is about 0.4 hectare, and a hectare is just under 2.5 acres.

10.6.6 Converting Between Area Units

10.6.8 Estimating Complicated Areas