A square has a perimeter of 12 cm. Six of these squares fit together to make a rectangle. What is the area of the rectangle?

Step-by-step solution

1. 1

   Turn the perimeter into a side length. A square has four equal sides, so its perimeter is $4s$. From $4s=12$ we get $s=\dfrac{12}{4}=3$ cm.

2. 2

   Find the area of one square. $A_{\text{square}}=s^2=3^2=9\text{ cm}^2$.

3. 3

   Use the fact that area adds. The six squares are fitted together without gaps or overlaps, so the rectangle's area is exactly the sum of the six square areas. No information about the arrangement is needed — a $1\times 6$ strip and a $2\times 3$ block give the same total.

4. 4

   Multiply. $A_{\text{rectangle}}=6\times 9=54\text{ cm}^2$.

5. 5

   Check with the two possible rectangles. A $2\times 3$ block of squares measures $6$ cm by $9$ cm, giving $6\times 9=54\text{ cm}^2$. A $1\times 6$ strip measures $3$ cm by $18$ cm, giving $3\times 18=54\text{ cm}^2$. Both confirm the answer.