2.3. Surface area Surface area is a quantity obtained by multiplying two lengths, which must be expressed in the same unit. For example: 5.40 m × 6.50 m = 35.10 m2 1 S O LV E D P R O B L E M 3 Write 0.5 dam2 in dm2. S O LV E D P R O B L E M 4 Write 85 cm2 in m2. For measurements of surface area : To obtain the next largest multiple, divide it by 100. For example: 500 cm2 = 5 dm2. To obtain the next smallest submultiple, multiply it by 100. For example: 3 m2 = 300 dm2. What do the factors in the table mean? 1. Identify the units. dam2 ® dm2 2. To move from one to the other, go towards the submultiples. The exponent of 100 will be positive. 3. Count the number of steps between the two units. This is the exponent of 100. dam2 m2 dm2 4. Write it in the corresponding unit. 0.5 dam2 = 0.5 × 1002 dm2 = 0.5 · 104 dm2 = 5 000 dm2 × 100 × 100 2 steps 1. Identify the units. cm2 ® m2 2. To move from one to the other, go towards the multiples. The exponent of 100 will be negative. 3. Count the number of steps between the two units. This is the exponent of 100. m2 dm2 cm2 4. Write it in the corresponding unit. 85 cm2 = 85 × 100-2 m2 = 85 × 10-4 m2 = 85 × 1 104 m2 = 0.0085 m2 : 100 2 steps : 100 Multiples 102 = 100 104 = 10 000 106 = 1 000 000 hundred ten thousand million 2 zeros 4 zeros 6 zeros Submultiples 10-2 = 1 102 = 1 100 = 0.01 10-4 = 1 104 = 1 10 000 = 0.0001 10-6 = 1 106 = 1 1 000 000 = 0.00 0001 hundredth ten thousandth millionth 2 zeros 4 zeros 6 zeros 20 Convert these amounts: a) 1.25 m2 ® cm2 b) 0.082 km2 ® dm2 c) 1.007 dam2 ® mm2 d) 500 cm2 ® dm2 21 Take a milk carton and calculate the surface area of each of its sides. What measurements should you take? Write the result in cm2 and m2. 22 A commonly used unit of surface area is the hectare (10 000 m2). How many hectares is a football pitch that is 100 m long and 70 m wide? 23 Order these amounts from largest to smallest: a) 1 432 cm2 347 dam2 0.0005 km2 b) 0.000 564 hm2 657 892 cm2 4.5 m2 A C T I V I T I E S Surface area km2 hm2 dam2 m2 dm2 cm2 mm2 : 100 : 100 : 100 : 100 : 100 : 100 × 100 × 100 × 100 × 100 × 100 × 100 Name Symbol Factor Unit Multiple kilo k × 106 km2 hecto h × 104 hm2 deca da × 102 dam2 Unit base m2 Submultiple deci d × 10-2 dm2 centi c × 10-4 cm2 mili m × 10-6 mm2 17
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