Area of a rectangle
Grade 4 students learn to calculate the area of a rectangle in Saxon Math Intermediate 4 Chapter 5 using the formula Area = length × width. The result is always expressed in square units, such as square feet (sq. ft) or square meters (sq. m). A garden 15 feet long and 5 feet wide has area 75 sq. ft; a poster 20 inches by 8 inches covers 160 sq. in. Unlike perimeter, which measures distance around, area measures the two-dimensional space inside—the total number of unit squares that fit within the rectangle.
Key Concepts
Property To find the area of a rectangle, you must multiply its length by its width. The formula is $\text{Area} = \text{length} \times \text{width}$. The result is always expressed in square units, such as square feet (sq. ft) or square meters (sq. m), representing the total space inside the shape's boundaries.
Example A rectangular garden is 15 feet long and 5 feet wide. Its area is $15 \text{ ft} \times 5 \text{ ft} = 75 \text{ sq. ft}$. To find the area of a poster that is 20 inches by 8 inches, multiply the sides: $20 \text{ in} \times 8 \text{ in} = 160 \text{ sq. in}$. A rectangular flag measures 11 meters by 7 meters. The total area inside the flag is $11 \text{ m} \times 7 \text{ m} = 77 \text{ sq. m}$.
Explanation Figuring out the area of a rectangle is like calculating how much wrapping paper you need for a gift. Just multiply the two side lengths! This handy trick tells you the total number of little squares that can fit inside the shape. It’s a super practical way to use multiplication for real world measurements and projects.
Common Questions
What is the formula for the area of a rectangle?
Area = length × width. Multiply the two perpendicular side lengths together. The result is expressed in square units, such as square centimeters (sq. cm) or square feet (sq. ft).
What are square units and why must area be expressed in them?
Square units (like sq. ft or sq. m) represent individual unit squares. When you multiply length by width, you are counting how many of those unit squares fit inside the rectangle, so the answer must use square units.
What is the difference between area and perimeter?
Perimeter is the total distance around the outside of a shape, measured in linear units like feet or meters. Area measures the space inside the shape, expressed in square units like sq. ft or sq. m.
How do you calculate the area of a 15 ft by 5 ft garden?
Apply the formula: Area = 15 ft × 5 ft = 75 sq. ft. The garden has 75 square feet of space inside its boundaries.
Can a rectangle have the same area as another rectangle but a different perimeter?
Yes. A 4 × 6 rectangle has area 24 sq. units and perimeter 20 units. A 3 × 8 rectangle also has area 24 sq. units but perimeter 22 units. Same area, different perimeter.
What real-world problems require finding the area of a rectangle?
Buying flooring or carpet for a room, calculating paint needed for a wall, finding how much sod to cover a lawn, or determining the size of a computer screen all require rectangular area calculations.