The area of a square tells us how much surface is enclosed inside its four equal sides. From floor planning to tiling, gardening to construction, this simple formula helps in many everyday tasks. In mathematics, it is one of the most basic and widely used geometry formulas, making it important for school-level chapters and competitive exams alike. Once you know the side of a square, calculating its area becomes quick and straightforward.
Area of a Square Formula Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| A = side² | side (a) = one side of the square | To find the total space covered inside a square |
What is the Area of a Square in Maths?
In mathematics, the area of a square means the measure of the total region inside the square. Because all four sides are equal, multiplying one side by itself gives the total area. The result is always expressed in square units like cm², m², or km².
A square is a special quadrilateral with four equal sides and four right angles. The formula to calculate its area is:
Area = side × side = side²
For example: If the side of a square is 5 cm, then
Area = 5 × 5 = 25 cm²
This formula is widely used in real life, measuring tiles, calculating land size, estimating painting area, or planning layouts. It is also a common topic in CUET, SSC, Banking, JEE, and school geometry exams. Always ensure the units are the same before calculating (for example, don’t use cm for one side and m for another).
Examples to Calculate Area of a Square
Example 1: Side = 12 cm
Step 1: Formula → Area = side × side
Step 2: Area = 12 × 12
Step 3: Area = 144 cm²
So, the area of the square is 144 cm².
Example 2: Side = 20 m
Step 1: Formula → Area = side × side
Step 2: Area = 20 × 20
Step 3: Area = 400 m²
So, the area of the square is 400 m².
FAQs about Area of a Square Formula
Q1. What is the area of a square?
It is the total space enclosed inside the four equal sides of a square.
Q2. Which unit is used for area?
Area is measured in square units like cm², m², or km².
Q3. Is the formula same for perimeter and area?
No. Perimeter = 4 × side, while Area = side².
Q4. Where do we use the area of a square in real life?
It is used in measuring floor space, garden plots, wall painting area, or land size.
Q5. Can we find the area if only perimeter is given?
Yes. First find the side = perimeter ÷ 4, then apply side².
Q6. Why is it called side squared?
Because you multiply the side by itself to get the area.