Area of a square

Here you will learn about finding the area of a square, including counting units squares and multiplying the side lengths.

Students will first learn about the area of a square as part of measurement and data in 3 rd grade.

What is the area of a square?

The area of a square is the amount of space inside the square. It is measured in square units.

For example,

The square units line up with all sides of the square and do not overlap. The area of the square is the number of square units within it.

Notice the connection between the side of a square and the square units:

The side length is always the same as the number of columns and rows of square units, since a square has equal sides.

This is why the area of square formula is \text {side} \times \text {side.}

For example,

Area is always labeled in square units. You can write it out or use the exponent 2 (a small 2 ) to show the units are square.

For example,

square centimeters (\mathrm{cm}^2), square meters (\mathrm{m}^2), square feet (\mathrm{ft}^2), square inches (\mathrm{in}^2).

The area of other polygons is also measured in square units.

For example,

The square units of the rectangle line up with the sides, just like they did for the square. There are 27 square units inside the rectangle, so that is the area.

Notice that this is not true for the other shapes. Some or all of their sides do not line up with the square units. Counting their square units is not as easy. This is why the area of a circle, triangle, hexagon and other shapes is covered in later grades.

What is the area of a square?

Common Core State Standards

How does this relate to 3 rd grade math?

• Grade 3 – Measurement and Data (3.MD.C.5)
  Recognize area as an attribute of plane figures and understand concepts of area measurement.
  a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
  b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

• Grade 3 – Measurement and Data (3.MD.C.6)
  Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

• Grade 3 – Measurement and Data (3.MD.C.7a)
  Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

How to find the area of a square

In order to find the area of a square by counting unit squares:

1. Be sure that the square is made of whole unit squares in an array.
2. Count the unit squares to find the area.

In order to calculate the area of a square:

1. Identify the side length of the square.
2. Write down the formula for the area of a square.
3. Substitute the given values and calculate.
4. Write down your final answer with units squared.

Area of a square examples

Example 1: counting unit squares to find the area

What is the area of the square?

1. Be sure that the square is made of whole unit squares in an array.

The unit squares inside the square line up with the sides of the square.

2Count the unit squares to find the area.

The area of the square is 9 square units.

Example 2: counting unit squares to find the area

What is the area of the square?

Be sure that the square is made of whole unit squares in an array.

The unit squares inside the square line up with the sides of the square.

Count the unit squares to find the area.

The area of the square is 36 square units.

Example 3: counting unit squares (and multiplying the sides) to find the area

What is the area of the square?

Identify the side length of the square.

Substitute the given values and calculate.

\text { Area }=7 \times 7=49

You can prove this by counting the unit squares within.

Example 4: counting unit squares (and multiplying the sides) to find the area

What is the area of the square?

Identify the side length of the square.

Substitute the given values and calculate.

\text { Area }=5 \times 5=25

You can prove this by counting the unit squares within.

Example 5: multiplying the sides to calculate the area

What is the area of the square?

Identify the side length of the square.

Since the length of the sides is the same, all sides are 8 \, cm.

Example 6: multiplying the sides to calculate the area

The wall above needs to be painted. How many square feet of paint is needed to cover the wall?

Identify the side length of the square.

Since the length of a side is the same as the others, all sides are 4 \, ft.

Teaching tips for area of a square

• Make sure students have plenty of practice with tiling squares to find the area (via manipulatives or a digital resource that allows them to do this). These opportunities can provide the conceptual understanding necessary to use the area formula.

• Worksheets can be a great source for practice, but be sure to use worksheets that provide a variety of practice (squares whose area can be found by using physical tiles and squares with or without grids).

Easy mistakes to make

• Confusing area and perimeter of a square
  When first learning about these two concepts, it can be easy to confuse them. Remember that perimeter is the distance around a square and can be found by adding all the sides up (or multiplying one side by 4 ) and area is the space within the square and can be found by multiplying two sides or counting the unit squares within.
  For example,
  
  

  

• Not using common units
  When tiling a shape to find the area, it is important that all the tiles are the same size. When solving area problems with real world measurements, it is important that all measurements are in the same unit. Having different size tiles or measurements will make the area calculation incorrect.

Related area of a quadrilateral lessons

• Area of a rectangle
• Area of a parallelogram
• Area of a trapezoid
• Area of a rhombus

The next lessons are

• Volume
• Surface area
• Pythagorean Theorem

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