Area of Rectangles and Squares

Geometry · Axiom Academy

LESSON Area of Rectangles and Squares Mastering the foundational area formulas — and seeing why they're really just counting unit squares. Area measures the space inside a shape, counted in unit squares. For a rectangle you have length columns and width rows of unit squares, so the count is length times width. A square is just a rectangle whose sides are equal. 2. Understanding Through Unit Squares The reason multiplication works: laying the rectangle out as a grid turns area into simple counting. Here a rectangle that is 5 units wide and 3 units tall holds exactly 5 × 3 squares. The length tells you how many unit squares fit in a single row — here, 5. The width tells you how many such rows stack up — here, 3. 5 columns × 3 rows = 15 squares, so . Each square is one square unit, so area is always in square units: cm², m², in², … Multiplying length by width is exactly the same as counting unit squares — it just skips the tedious part. That's why the rectangle is the foundation every other area formula builds on. A rectangle has length 12 cm and width 8 cm . Find its area. Apply the formula directly — substitute the two dimensions and multiply. 4. Example: Finding a Missing Dimension The formula runs backward too. A rectangle has area 72 m² and length 9 m . To recover a missing side, divide the area by the dimension you know.

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