How do you find the area of a square?



Geometry is a very important branch of mathematics which deals with size, shape, the relative position of shapes, and the properties of figures. The geometry basically deals with the practical application of various shapes such as area, volume, and surface area of the different figures or shapes. It can be broadly categorized into two different types, i.e., Solid Geometry and Plane Geometry. The Plane Geometry generally discuss the shapes such as triangles, circles, square, rectangles, and many more. Whereas, Solid Geometry involves the calculating of the length, area, perimeter, as well as the volume of various geometric shapes and figures.

It is often observed that many students get confused with the term area or find it difficult to understand the concept of area. Basically, in geometry, the area is the amount of space takes up on a plane by a flat geometric shapes shape like a square, polygon, circle triangle, ellipse, etc. For most of the geometrical shapes we consider the height and width of the shape on the plane. 

You need to understand the definition and the shape of the geometric figures before understanding the concept of area. So, what is a square? A square is quadrilateral-shaped closed, two-dimensional shape with 4 equal sides. Here are the properties of square:

  • All the sides of the square are equal in dimensions. 
  • Each of the interior angle (Total 4 interior angle) are 90oOpposite sides of a square are parallel to each other. 
  • The diagonals of a square are equal. 

Now, coming to your question. In simple words, the area of a square is the number of square units required to fill a square. As I have already mentioned, the area is defined as the space occupied inside the boundary of a 2d figure or flat figure. The dimension is measured in square units with the standard unit being meters square (m2). 

The formula to calculate the area of a square is, Area = (Side)2 

Let’s try to understand it with the help of an example. Suppose the side of a square is measured to be 3 m. I have already mentioned that all the sides of the square are equal in demotion. Therefore, the dimensions of the other sides will be 3 m each. Now the area of the square will be, Area= (3)2= 9 m2 or we can write it as Area = 3 m x 3 m =9 m2

You can derive the formula for the area of the square from the area of the rectangle formula. 

As we know that, the area of a rectangle is = Length x breadth. 

Since the length and breadth are equal in a square, we can rewrite the formula for square as = side x side which is (Side)2

Here is some practical applications related problem of the area of a square. Try to understand these solved examples. It will help you understand the concept more clearly. 

  1. Calculate the area of a square board whose side measures 110 cm.


Given, side of the clipboard = 100 cm = 1.1 m (Always convert the units to the meter)

we know that, Area of the square = side × side

= 1.1 m × 1.1 m 

= 1.21 sq. m or 1.21 m2 

  1. The side of a wall whose shape is square is measured to be 70 m. find out the cost of painting it at the rate of Rs. 2 per sq. m?


Given, the shape of the wall is square. 

Side of the wall = 70 m

We know that, area of a square = side × side

Therefore, area of the wall = 70 m × 70 m = 4900 sq. m

Given, the cost of painting for 1 sq. m = Rs. 2

Thus, for 4900 sq. m, the cost of painting = Rs. 2 × 4900 = Rs 9800

Therefore, you need to spend Rs 9800 to paint a square wall whose side is 70 m. 

In this way, you can use the concept of area in practical applications. Try to relate the concepts of mathematics with some practical applications. It will help you to understand the concepts more easily.