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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:

Rectangle

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.

Rectangle

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:

    5x1 rectangle

    7. Find the area of the rectangle below:

    7x2 rectangle

    8. Find the area of the rectangle below:

    6x1 rectangle

    9. Find the area of the square below:

    2x2 square

    10. Find the area of the square below:

    8 in square

    Answer Key:

Test Prep Practice

  • Rectangles: Area

    1. Find the area of a square that has a perimeter of 60 centimeters.

    a. 15 cm2
    b. 20 cm2
    c. 200 cm2
    d. 225 cm2

    2. Find the area of a square that has a perimeter of 120 centimeters.

    a. 30 cm2
    b. 90 cm2
    c. 200 cm2
    d. 900 cm2

    3. Find the area of a square whose perimeter is 24 inches.

    a. 6 in2
    b. 18 in2
    c. 24 in2
    d. 36 in2

    4. Find the area of a square whose perimeter is 48 feet.

    a. 24 ft2
    b. 48 ft2
    c. 144 ft2
    d. 1220 ft2

    Use the figure below to answer the rest of the questions:

    Rectangle with length 10

    5. If the rectangle above has a perimeter of 50 cm, what is the width of the rectangle?

    a. 10 cm
    b. 15 cm
    c. 20 cm
    d. 30 cm

    6. If the rectangle above has a perimeter of 80 cm, what is the area of the rectangle?

    a. 30 cm2
    b. 60 cm2
    c. 300 cm2
    d. 900 cm2

    7. If the rectangle above has an area of 100 cm2, what is the perimeter of the rectangle?

    a. 40 cm2
    b. 80 cm2
    c. 1600 cm2
    d. 6400 cm2

    8. If the rectangle above has an area of 300 cm2, what is the width of the rectangle?

    a. 10 cm
    b. 30 cm
    c. 75 cm
    d. 100 cm

    9. If the rectangle above has a width of 20 cm, what is the area of the rectangle?

    a. 160 ft2
    b. 180 ft2
    c. 200 ft2
    d. 400 ft2

    10. If the rectangle above has an area of 150 cm2, what is the width of the rectangle?

    a. 12 cm
    b. 15 cm
    c. 25 cm
    d. 100 cm

    Answer Key: