Area of a Square Notes

Published on: September 29, 2026

This Area of a Square Calculator finds the space inside a square from the length of one side, and shows the working line by line. A square has four sides of the same length, so a single measurement describes the whole shape. Squaring that side length counts the unit squares that fill it, and the answer is written in square units. Following the same pattern every time is what makes the area of a square easy to picture, check, and work out on your own for any side length.

In the diagram, each side is labeled \(a\).

Step-by-step method

Set up the problem.
Write the formula.
Substitute the side length into the formula.
Work out the area.

Formula:

\(A = a^{2}\)

See Example 1 Hide Example 1

Problem

\(a = 8\)

Approach

Step-by-step method

Set up the problem.
Write the formula.
Substitute the side length into the formula.
Work out the area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the area of a square whose side length is \(a = 8\).

\(a = 8\)

Step 2

Step 2 - Write the formula.

In this problem: A square has four sides of the same length, so its area is that side length multiplied by itself.

\(A = a^{2}\)

Step 3

Step 3 - Substitute the side length into the formula.

In this problem: Replacing \(a\) with \(8\) in \(A = a^{2}\) gives \(A = 8^{2}\).

\(A = 8^{2}\)

Step 4

Step 4 - Work out the area.

In this problem: \(8^{2}\) means \(8 \times 8\), and \(8 \times 8 = 64\).

\(A = 8^{2} = 64\)

Final Answer

\(A = 64\)

See Example 2 Hide Example 2

Problem

\(a = 2.5\)

Approach

Step-by-step method

Set up the problem.
Write the formula.
Substitute the side length into the formula.
Work out the area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the area of a square whose side length is \(a = 2.5\).

\(a = 2.5\)

Step 2

Step 2 - Write the formula.

In this problem: A square has four sides of the same length, so its area is that side length multiplied by itself.

\(A = a^{2}\)

Step 3

Step 3 - Substitute the side length into the formula.

In this problem: Replacing \(a\) with \(2.5\) in \(A = a^{2}\) gives \(A = 2.5^{2}\).

\(A = 2.5^{2}\)

Step 4

Step 4 - Work out the area.

In this problem: \(2.5^{2}\) means \(2.5 \times 2.5\), and \(2.5 \times 2.5 = 6.25\).

\(A = 2.5^{2} = 6.25\)

Final Answer

\(A = 6.25\)

See Example 3 Hide Example 3

Problem

\(a = 6\)

Approach

Step-by-step method

Set up the problem.
Write the formula.
Substitute the side length into the formula.
Work out the area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the area of a square whose side length is \(a = 6\).

\(a = 6\)

Step 2

Step 2 - Write the formula.

In this problem: A square has four sides of the same length, so its area is that side length multiplied by itself.

\(A = a^{2}\)

Step 3

Step 3 - Substitute the side length into the formula.

In this problem: Replacing \(a\) with \(6\) in \(A = a^{2}\) gives \(A = 6^{2}\).

\(A = 6^{2}\)

Step 4

Step 4 - Work out the area.

In this problem: \(6^{2}\) means \(6 \times 6\), and \(6 \times 6 = 36\).

\(A = 6^{2} = 36\)

Final Answer

\(A = 36\)

See Example 4 Hide Example 4

Problem

\(a = 4.5\)

Approach

Step-by-step method

Set up the problem.
Write the formula.
Substitute the side length into the formula.
Work out the area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the area of a square whose side length is \(a = 4.5\).

\(a = 4.5\)

Step 2

Step 2 - Write the formula.

In this problem: A square has four sides of the same length, so its area is that side length multiplied by itself.

\(A = a^{2}\)

Step 3

Step 3 - Substitute the side length into the formula.

In this problem: Replacing \(a\) with \(4.5\) in \(A = a^{2}\) gives \(A = 4.5^{2}\).

\(A = 4.5^{2}\)

Step 4

Step 4 - Work out the area.

In this problem: \(4.5^{2}\) means \(4.5 \times 4.5\), and \(4.5 \times 4.5 = 20.25\).

\(A = 4.5^{2} = 20.25\)

Final Answer

\(A = 20.25\)