10.6.6 Converting Between Area Units

In the previous section, we stressed the importance of using the same units all the way through a calculation. However, there may be occasions when you need to convert from one square unit to another. For example, if you want to find the area of a piece of land from a map, you could measure the area in square centimeters on the map, but this would be an inappropriate unit for the amount of land itself.

To change from one square unit to another, you need to know how many of the smaller units are equivalent to one of the larger units. For example, how many square millimeters are needed to cover one square centimeter?

If you are not sure, a diagram might help.

If you draw a square centimeter and imagine covering it with square tiles that each have an area of 1 millimeter square left parenthesis one times mm super two right parenthesis, you would be able to fit 10 of the 1 mm square tiles along the bottom edge of the 1 cm square tile, since there are 10 mm in 1 cm. Then you would be able to fit nine further rows each of 10 1 mm square tiles next to the first row. So 10 rows, each with ten 1 mm square tiles, would be needed to cover 1 square centimeter.

In other words, there are 100 square millimeters in 1 square centimeter:

one times cm super two equals 10 mm multiplication 10 mm equals 10 equation left hand side prefix multiplication of 10 times mm super two equals right hand side 100 times mm super two

Activity Symbol Activity: Converting Square Units

(a) Explain how many square centimeters are equivalent to one square meter.

Solution Symbol

Answer

(a) One square meter is 100 cm long and 100 cm wide. So we could fit 100 1 cm square tiles along the edge of a square meter tile. But you could then fit 99 more rows of the small tiles above this row.

So altogether, there would be 100 rows of 100 small tiles or 10,000 small tiles. In other words, one times m super two equals 10 comma 000 times cm super two.

(b) Convert 6000 times cm super two into m super two.

Hint symbol

Comment

Think about whether your answer should be bigger or smaller than the original value.

Solution Symbol

Answer

(b) Since there are 10 comma 000 times cm super two in one times m super two and we are converting from a small unit to a larger one, we need to divide

six comma 000 times cm super two equals six comma 000 division 10 comma equation left hand side 000 times m super two equals right hand side 0.6 times m super two

(c) Convert eight times cm super two into mm super two.

Solution Symbol

Answer

(c) Since there are 100 times mm super two in one times cm super two and we are converting from a large unit to a smaller one, equation sequence 0.85 times cm super two equals 0.85 multiplication 100 times mm super two equals 85 times mm super two.

(d) How many square meters are equivalent to 1 square kilometer?

Hint symbol

Comment

Draw a diagram representing a square kilometer.

Solution Symbol

Answer

(d) Since there are 1,000 m in 1 km, 1 square kilometer is the same as one comma 000 multiplication one comma 000 meters, or one times km super two equals one comma 000 comma 000 times m super two.

10.6.5 Making a Garden

10.6.7 Estimating Areas