Area with Decimal Side Lengths

Finding the area of a shape tells us how much space is inside it. You probably already know how to find the area of a rectangle using whole numbers, but what happens when the sides are measured in decimals? The process is exactly the same!

The Area Formula

To find the area of a rectangle, you multiply its length ($l$) by its width ($w$). $A = l \times w$ Area is always measured in "square units" (like square meters, $m^2$, or square feet, $ft^2$).

Calculating Area with Decimals

Let's look at an example: Find the area of a rectangle that is $3.5$ m by $2.4$ m.

1. Set up the equation using the area formula: $A = 3.5 \times 2.4$
2. Multiply the numbers as if they were whole numbers: $35 \times 24 = 840$
3. Count the total number of decimal places in your original factors. Both $3.5$ and $2.4$ have one decimal place, making a total of two decimal places.
4. Place the decimal point two spots from the right in your answer: $8.40$ (or just $8.4$).

The area is $8.4$ square meters ($8.4 \text{ m}^2$).

Real-World Word Problems

Area calculations are incredibly useful for everyday projects like flooring, painting, and gardening. When a problem asks "how much surface needs to be covered," you are looking for the area.

Example: A yard is $12.5$ ft long and $8$ ft wide. How much sod (grass) is needed to cover the entire yard?

• Formula: $A = 12.5 \times 8$
• Multiply: $125 \times 8 = 1000$
• Place the decimal point (one decimal place in $12.5$): $100.0$

You will need $100$ square feet of sod.

Perimeter vs. Area

A common question in geometry is: If two rectangles have the same perimeter, do they have the same area?

The answer is no. Let's prove it:

• Rectangle 1: $5$ m by $3$ m.
  • Perimeter = $5 + 5 + 3 + 3 = 16$ m
  • Area = $5 \times 3 = 15 \text{ m}^2$
• Rectangle 2: $6$ m by $2$ m.
  • Perimeter = $6 + 6 + 2 + 2 = 16$ m
  • Area = $6 \times 2 = 12 \text{ m}^2$

Even though both rectangles have a perimeter of $16$ m, their areas are completely different!