Grade 6 Math: Area of Rectangles and Squares

Grade 6 focus: The area of a rectangle is the number of unit squares that cover it. The formula is \(A = \ell \times w\) (length times width). A square with side length \(s\) has area \(A = s^2\).

Video lesson: Watch this Math with Mr. J tutorial on area of rectangles and squares.

Units matter

Area is in square units (square inches, square meters, etc.). If sides are in inches, area is in square inches.

Decimals and fractions

Multiply as with whole numbers, then count decimal places—or multiply numerators and denominators for fractional side lengths.

Example: rectangle \(2.5\) m by \(4\) m: \(A = 2.5 \times 4 = 10\) square meters.

Squares

For a square with side \(3\frac{1}{2}\) ft, \(A = \left(3\frac{1}{2}\right)^2 = \left(\frac{7}{2}\right)^2 = \frac{49}{4} = 12\frac{1}{4}\) square feet.

Common mistakes

• Confusing perimeter (\(2\ell + 2w\)) with area (\(\ell \times w\)).
• Forgetting to square the side for a square’s area.
• Mixing linear units with area units.

Real-world link

Flooring, painting, and tiling problems often ask for area—estimate first, then compute.

Step-by-Step Guide to Finding Area

The area of a rectangle or square is one of the most fundamental concepts in geometry. To find the area, we multiply the length by the width. For rectangles, \(A = l \times w\), where \(l\) is the length and \(w\) is the width. For squares, since all sides are equal, \(A = s^2\), where \(s\) is the side length.

Worked Examples: Area Calculations

Example 1: A rectangle has a length of 8 cm and a width of 5 cm. The area is \(A = 8 \times 5 = 40\) square centimeters.

Example 2: A square has sides of 6 inches. The area is \(A = 6^2 = 36\) square inches.

Common Mistakes to Avoid

• Forgetting to multiply length and width
• Confusing perimeter with area
• Using the wrong units in your answer
• Not aligning units before calculating

Related Topics to Explore

• Area of Parallelograms
• Area of Triangles
• Finding Area of Compound Figures

Practice Problems

1. Find the area of a rectangle with length 12 cm and width 9 cm.
2. A square garden has sides of 15 meters. What is the total area?
3. If a rectangular room has an area of 120 square feet and a length of 15 feet, what is the width?