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Square Area Calculator

Introduction

Welcome to our Square Area Calculator! which will help you calculate the square’s area quickly and accurately. A Square is a four-sided polygon where all four sides are equal. So, the square’s four sides make equal angles at its vertices, measuring 90 degrees each.

The total space occupied by the square is called the area of the square. The area of the square is dependent on the length of its sides.

How to use this Calculator?

Using the Square Area Calculator, you can calculate the area of the square by using two methods.

Area of Square using Length of Sides

You can calculate the area of the square if you know the length of the side.

The variables in the calculator include:

Side of Square (a) The length of one side of a square.

Area of Square (Area) We can calculate the area of the square using the following formula

Area=a×a=a2\text{Area} = a \times a = a^2

Area of Square using Length of Diagonal

You can also calculate the area of the square using the length of the diagonal.

The variables in the calculator include:

The diagonal of Square (d) The length of the Diagonal of the Square.

Area of Square (Area) We can calculate the area of the square using the following formula

Area=Diagonal22=d22\text{Area} = \normalsize \dfrac{\text{Diagonal}^2}{2} \\[10pt] = \normalsize \dfrac{d^2}{2}

What is a Square?

A Square is a two-dimensional shape with four equal sides and four equal right angles at its vertices. The square’s diagonals are also equal in length and perpendicular bisectors of each other.

We are going to list the properties of a square which include

  1. All four sides are equal.

  2. All angles measure 90 degrees.

  3. Opposite sides of a Square are parallel to each other.

  4. The sum of all interior angles is 360 degrees.

  5. The length of the diagonals of a square is equal.

  6. The diagonals of a square bisect each other at 90 degrees.

The Square is a fundamental shape in geometry, and it helps us understand various concepts of geometry like area and perimeter and also in other fields like engineering for structural design, architecture and even software engineering to represent digital objects. In addition, some of the real-world examples of squares can be found in papers, tiles, boxes, etc

How is the Area of the Square Calculated?

The area of a square is defined as the space taken up by the shape. It could also be thought of as the number of square units required to fill the region inside the square. Hence the measurement will be in square units.

Basically, the area of the square can be calculated in two ways:

  1. Area of Square using Length of Sides

  2. Area of Square using Length of Diagonal

Area of Square using Length of Sides

The basic formula to calculate the area of the square is by multiplying the length of the two sides. Since the square has equal sides, the area will be equal to the square of the side.

Area=a×a=a2\text{Area} = a \times a = a^2

Where

a = Length of the side of a square

Area of Square using Length of Diagonal

Another method to calculate the area of the square is by using the length of the diagonal of the square.

Area=Diagonal22=d22\text{Area} = \normalsize \dfrac{\text{Diagonal}^2}{2} \\[10pt] = \normalsize \dfrac{d^2}{2}

Where,

d = Length of the diagonal of the Square.

Examples

Example 1

Let’s say there is a square with a length of a side equal to 5 cm, what is the area of the square?

The area of the square can be calculated using the following formula.

Area=5  cm×5  cm=52=25  cm2\begin{aligned} \text{Area} &= 5 \;cm \times 5 \; cm = 5^2 \\ &= 25 \; cm^2 \end{aligned}

As shown above, in the example we multiply two sides of the square to get the area of the square which is  25 sq cm

Example 2

Let’s there is a square with a diagonal of 8cm, calculate the area of the square.

The area of the square can be calculated using the following formula

Area=Diagonal22=822=32  cm2\begin{aligned} \text{Area} &= \normalsize \dfrac{\text{Diagonal}^2}{2} \\[10pt] &= \normalsize \dfrac{8^2}{2} \\[10pt] &= 32 \; cm^2 \end{aligned}

As shown above, in the example, we can see how to calculate the area of the square by using the length of the diagonal.

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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