Area of the Square - Examples, Exercises and Solutions

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=side2Area=side^2

Let's take this square as an example:

A1- The area of a square

The area will be: A=a×a A=a\times a or A=a2A=a^2
where AA: represents the area of the square
and aa –> is the length of the edge (or side) of the square

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

A=Diagonal×Diagonal2A = \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:

141414

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:

555

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=a2 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=52=25 S=5^2=25

Answer:

25 25

Video Solution
Exercise #2

Look at the square below:

999

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=L2 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=92=81 A=9^2=81

Answer:

81 81

Video Solution
Exercise #3

Given the square:

777

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=L2 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=72=49 A=7^2=49

Answer:

49 49

Video Solution
Exercise #4

Look at the square below:

333

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=L2 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=32=9 A=3^2=9

Answer:

9 9

Video Solution
Exercise #5

Look at the square below:

101010

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=L2 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=102=100 A=10^2=100

Answer:

100 100

Video Solution

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