The diagram shows a square with a perimeter of 12cm. Six of these squares fit together to make a rectangle. What is the area of the rectangle?

Question

perimeter of rectangle is 30cm, how do I convert to area quickly and easily?

Answer 1

A square with a 12 cm perimeter has 4 sides of equal length, so each side of the square is 3 cm long.  There are only two unique ways to arrange these square tiles into a rectangle: 1x6 or 2x3 (based on possible factor pairs of the number 6).  1(3) + 6(3) + 1(3) + 6(3) = 3+18+3+18 = 42 cm perimeter for the 1x6 rectangle, and 2(3) + 3(3) + 2(3) + 3(3) = 6+9+6+9 = 30 cm perimeter for the 2x3 rectangle, so we know it's the 2x3 rectangle that we want.   That rectangle has sides of length 6 cm and 9 cm (2 x 3 cm for one side and 3 x 3 cm for the other), and to get the area we multiply them together.   6 x 9 = 54.  The area is 54 square cm.