Areas of Rectangles
The area of a rectangle equals its length multiplied by its width (A = l × w), expressed in square units. In Grade 6 Saxon Math Course 1 (Chapter 4: Number, Operations, and Measurement), students apply this formula to real-world situations such as calculating carpet area or garden space. A rectangle 8 cm long and 5 cm wide has an area of 40 cm². Students also work backwards: given area and one side, divide to find the missing dimension. They distinguish area (square units, measuring flat space inside) from perimeter (linear units, measuring the boundary).
Key Concepts
New Concept The area of a shape is the amount of surface enclosed by its sides. We calculate a rectangle's area by multiplying its length and width.
$$ \text{Length} \times \text{width} = \text{area} $$ What’s next This is just the beginning of measuring surfaces. Next, you'll solve problems to find the area of rectangles and squares, and even work backward to find side lengths.
Common Questions
What is the formula for the area of a rectangle?
Area = length × width. Both dimensions must use the same unit, and the result is in square units such as cm², m², or ft².
What are square units and why are they used for area?
Square units count how many unit squares fit inside a shape. Since area measures two-dimensional flat space, the unit must be squared. For example, 6 cm × 4 cm = 24 cm².
How do you find a missing side of a rectangle when you know the area?
Divide the area by the known side. If area = 48 m² and width = 6 m, then length = 48 ÷ 6 = 8 m.
What is the difference between area and perimeter of a rectangle?
Area measures flat space inside using the formula length × width in square units. Perimeter measures the total boundary distance using 2l + 2w in linear units.
A rectangle is 12 feet long and 7 feet wide. What is its area?
Area = 12 × 7 = 84 square feet.