Area of a Square Practice Problems with Solutions

Master calculating square area using side length and diagonal formulas. Practice with step-by-step solutions and real-world examples to build confidence.

📚What You'll Master in This Practice Session

Apply the formula A = side² to calculate square areas accurately
Use diagonal measurements to find square area with A = (d × d)/2
Solve real-world problems involving square measurements and units
Convert between different units when calculating square areas
Identify the relationship between square perimeter and area calculations
Work with both whole numbers and decimal measurements confidently

Understanding Area of the Square

Complete explanation with examples

Area of a Square

The area of a square represents the amount of space inside its four equal sides. It is calculated using the formula:

$Area=side^2$

Let's take this square as an example:

The area will be: $A=a\times a$ or $A=a^2$
where $A$ : represents the area of the square
and $a$ –> is the length of the edge (or side) of the square

Another way to calculate the square's area is by the diagonals:

$A = \frac{Diagonal \times Diagonal}{2}$

A1 - A represents the area of the square

Detailed explanation

Practice Area of the Square

Test your knowledge with 17 quizzes

Look at the square below:

What is the area of the square equivalent to?

Examples with solutions for Area of the Square

Step-by-step solutions included

Exercise #1

Look at the square below:

What is the area of the square equivalent to?

Step-by-Step Solution

The area of a square is equal to the square of its side length.

In other words:

$S=a^2$

Since in the diagram we are given one side of the square, and in a square all sides are equal to each other, we will solve for the area of the square as follows:

$S=5^2=25$

Answer:

$25$

Video Solution

Exercise #2

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$ Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=9^2=81$

Answer:

$81$

Video Solution

Exercise #3

Given the square:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=7^2=49$

Answer:

$49$

Video Solution

Exercise #4

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the diagram provides us with one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=3^2=9$

Answer:

$9$

Video Solution

Exercise #5

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=10^2=100$

Answer:

$100$

Video Solution

Frequently Asked Questions

Everything you need to know about Area of the Square

What is the formula for finding the area of a square?

The area of a square is calculated using the formula A = side², where A represents the area and 'side' is the length of any one side of the square. Since all sides of a square are equal, you simply multiply the side length by itself.

How do you find the area of a square using its diagonal?

You can calculate a square's area using its diagonal with the formula A = (diagonal × diagonal)/2. This method is useful when you only know the diagonal measurement and need to find the total area.

What units are used when measuring the area of a square?

Square area is always measured in square units such as: • Square centimeters (cm²) • Square meters (m²) • Square inches (in²) • Square feet (ft²) The unit depends on what unit was used to measure the original side length.

Why do we square the side length to find a square's area?

We square the side length because area represents the amount of space inside a shape. For a square, this means multiplying length × width, but since all sides are equal, we're essentially multiplying side × side, which equals side².

How is finding the area of a square different from finding the area of a rectangle?

A square is actually a special type of rectangle where all sides are equal. While a rectangle uses A = length × width, a square simplifies to A = side² since length and width are the same measurement.

What are common mistakes when calculating square area?

Common mistakes include: 1. Forgetting to square the side length (just using the side length as the answer) 2. Using incorrect units (linear units instead of square units) 3. Confusing area formulas with perimeter formulas 4. Not converting units properly before calculating

Can you find the side length if you know the area of a square?

Yes! If you know the area, you can find the side length by taking the square root of the area. The formula becomes: side = √area. For example, if the area is 25 cm², then the side length is √25 = 5 cm.

How do you solve word problems involving square area?

Follow these steps: 1. Identify what information is given (side length, diagonal, or area) 2. Determine what you need to find 3. Choose the appropriate formula (A = side² or A = diagonal²/2) 4. Substitute the known values and solve 5. Include proper units in your final answer

Continue Your Math Journey

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Area of a Square Practice Problems with Solutions

Understanding Area of the Square

Area of a Square

Practice Area of the Square

Examples with solutions for Area of the Square

Frequently Asked Questions

What is the formula for finding the area of a square?

How do you find the area of a square using its diagonal?

What units are used when measuring the area of a square?

Why do we square the side length to find a square's area?

How is finding the area of a square different from finding the area of a rectangle?

What are common mistakes when calculating square area?

Can you find the side length if you know the area of a square?

How do you solve word problems involving square area?

More Area of the Square Questions

Area of the Square

Continue Your Math Journey

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