Calculate the area of a rectangle measuring 4 m by 3 m.

Step-by-step solution

1. 1

   Use the rectangle area formula.

   $A=\text{length}\times\text{width}$

2. 2

   Substitute the given side lengths.

   $A=4\ \text{m}\times 3\ \text{m}=12$

3. 3

   Give the unit as square metres.

   $A=12\ \text{m}^2$

   Multiplying metres by metres produces m$^2$; writing the answer as $12$ m would describe a length, not an area.

4. 4

   See why the multiplication counts squares. Draw the rectangle as a grid: $4$ columns each $1$ m wide and $3$ rows each $1$ m tall. That is $4\times 3=12$ unit squares, each of area $1$ m$^2$ — so the formula is literally a count, not an abstract rule.

5. 5

   Compare with the perimeter to keep the two ideas separate. The perimeter is $2(4+3)=14$ m, a one-dimensional quantity in plain metres. Doubling both sides to $8$ m by $6$ m would double the perimeter to $28$ m but quadruple the area to $48$ m$^2$ — the classic scaling distinction between length and area.