# Rectangles: Area

The area of a shape is the size of the area inside the boundaries of that two-dimensional shape (once you start working with three dimensional shapes, area will refer to the two-dimensional area of one of the faces of that shape).

Finding the area of a rectangle simply requires you to find the two dimensions of the rectangle (length and width) and multiply them together:

Units for area are always square units (e.g., square inches ($\text{in}^2$) or square feet ($\text{ft}^2$)).

*Example: *Find the area of the rectangle below.

The length of the rectangle is 10: $l=10$

The width of the rectangle is 6: $w=6$

Note: Either side can be the length or the width, it doesn't matter, just make sure you choose different sides for the length and width, not parallel sides.

$$\eqalign{\text{area}&=\text{length}\times\text{width}\\a&=10\times6\\a&=60 \text{ units}^2}$$

Special note about squares: squares are rectangles! So, the area formula for squares is $a=l\times w$, but because all of the sides of a square are the same, you can use the same measure for length and width.

Finding the area of a rectangle is easy: identify the length and width and multiply them together.

**Note: **Make sure your units are the same (or in the unit you want your answer to be) before you multiply! It's always easier to convert linear units than square units!

**Also note:** Sometimes, to find the area of a rectangle, you have to do some work to find the length and width (most commonly, take apart the perimeter in some way). This isn't hard, just take it step by step (and review the Perimeter Lesson if you need to).

#### Practice Problems:

## Rectangles: Area

1. Find the area of a rectangle with width 7 inches and length 9 inches.

2. Find the area of a rectangle with length 9 feet and width 10 feet.

3. Find the area of a square with side 4 feet.

4. Find the area of a rectangle with width 2 feet and height 6 inches.

5. Find the area of a rectangle with length 1 yard and height 2 feet.

6. Find the area of the rectangle below:

7. Find the area of the rectangle below:

8. Find the area of the rectangle below:

9. Find the area of the square below:

10. Find the area of the square below:

#### Answer Key: