Calculate the area of a rectangle measuring 50 cm by 70 cm, and express the result in square metres as well.

Step-by-step solution

1. 1

   Use the rectangle area formula. For any rectangle,

   $A=\text{base}\times\text{height},$

   provided the two measurements are perpendicular sides expressed in the same unit. Here both are already in centimetres, so no conversion is needed before multiplying.

2. 2

   Multiply the numbers and the units together. Units multiply just like numbers do:

   $A=50\text{ cm}\times70\text{ cm}=3500\text{ cm}^{2}.$

   The answer is in square centimetres — writing $3500\text{ cm}$ would describe a length, not an area, and is the most common mistake on this kind of question.

3. 3

   Check the arithmetic a second way. Factoring out the tens: $50\times70=5\times7\times100=3500$ ✓. Estimating also helps — the rectangle is a bit smaller than $50\times100=5000$, and $3500$ sits sensibly below that.

4. 4

   Convert to square metres correctly. Since $1\text{ m}=100\text{ cm}$, squaring both sides gives $1\text{ m}^{2}=10\,000\text{ cm}^{2}$ — the conversion factor for area is the square of the length factor:

   $A=\frac{3500}{10\,000}\text{ m}^{2}=0.35\text{ m}^{2}.$

   Dividing by $100$ instead of $10\,000$ would give a hundredfold error.

5. 5

   Sanity-check the size. A $0.5\text{ m}\times0.7\text{ m}$ rectangle should have area $0.5\times0.7=0.35\text{ m}^{2}$ ✓ — computing entirely in metres from the start gives the same result, which confirms both the multiplication and the unit conversion.