Counting unit squares one by one is slow. But the squares in a rectangle form an array, and you know how to count arrays fast.
Por qué funciona
If a rectangle is 6 units long, 6 unit squares fit along it in one row. If it is 4 units wide, 4 such rows fit. That is an array of 4 rows of 6, so the number of squares is $4 \times 6$. The side lengths tell you the rows and columns without drawing a single square.
Idea clave
Area of a rectangle = length $\times$ width. The answer is in square units.
Ejemplo resuelto: Use the side lengths
A rectangle is 6 cm long and 4 cm wide. What is its area?
- 4 rows of 6 square centimeters.
- $4 \times 6 = 24$.
Respuesta: 24 square cm
Ejemplo resuelto: A rug
A rug is 9 feet long and 7 feet wide. What is its area?
- $9 \times 7 = 63$.
Respuesta: 63 square feet
Ejemplo resuelto: Missing side
A rectangle has an area of 24 square meters. One side is 4 meters. How long is the other side?
- $4 \times \square = 24$.
- $4 \times 6 = 24$.
Respuesta: 6 meters
Error común
Forgetting the "square." The sides are in centimeters, but the area counts squares, so it is in square centimeters. 24 cm would be a length; 24 square cm is an area.