Area for 5th Grade: Squares, Rectangles, and Composite Figures

Area is the amount of surface inside a two-dimensional shape. In Grade 5, students find the area of rectangles and squares using the formula length × width (or side × side for a square). Area is measured in square units—square centimeters (cm²), square meters (m²), square feet (ft²), etc. Area is used when covering a floor with carpet, painting a wall, buying grass for a lawn, or determining how much space a shape covers.

For a rectangle, the area is length × width because we count how many unit squares fit inside—if the length is 8 cm and the width is 5 cm, we have 8 rows of 5 squares each, so 8 × 5 = 40 square cm. For a square, area = side × side = s².

DETAILED EXPLANATION

Area of rectangle: \(A = l \times w\), where l = length and w = width.

Area of square: \(A = s \times s = s^2\), where s = side length.

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Units: Area is measured in square units (cm², m², ft², etc.).

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

A rectangle has length 8 cm and width 5 cm. Find the area.

Solutions:

Step 1: The area of a rectangle is \(A = \text{length} \times \text{width}\).

Step 2: Substitute: \(A = 8 \times 5 = 40\).

Step 3: The area is 40 square centimeters (or 40 cm²).

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Answer: 40 square cm (or 40 cm²)

Example 2

A square has side length 6 m. Find the area.

Solutions:

Step 1: The area of a square is \(A = \text{side} \times \text{side} = s^2\).

Step 2: Substitute: \(A = 6 \times 6 = 36\).

Step 3: The area is 36 square meters.

Answer: 36 square meters (or 36 m²)

Example 3

A garden is 12 feet by 9 feet. How many square feet of grass is needed?

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Solutions:

Step 1: Area = length × width.

Step 2: \(A = 12 \times 9 = 108\).

Step 3: 108 square feet of grass is needed to cover the garden.

Answer: 108 square feet

Example 4

A poster is 24 inches long and 18 inches wide. What is its area?

Solutions:

Step 1: \(A = 24 \times 18\).

Step 2: \(24 \times 18 = 432\).

Answer: 432 square inches