Area of a Square

Area of a square is defined as the number of square units needed to fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or 2d figure. The measurement is done in square units, with the standard unit being square metres (m²).

For the computation of area, there are pre-defined formulas for squares, rectangles, circles, triangles, etc. In this article, you will learn about the area of a square.

What is Area?

The area is the space covered by the object. It is the region occupied by any shape. While measuring the area of a square, we consider only the length of its side. All sides of a square are equal; hence, its area is equal to the square of the side.

Similarly, we can find the area of the other shapes such as rectangles, parallelograms, triangles or any polygon, based on its sides. The area of the surface is calculated based on the radius or the distance of its outer line from the axis for curved surface objects.
Example: circle

Learn more: What is mathematics?

Area of a Square Formula

Before moving into the area of square formula used for calculating the region occupied, let us try using graph paper. You are required to find the area of a side 5 cm. Using this dimension, draw a square on a graph paper having 1 cm × 1 cm squares. The square covers 25 complete squares.

Thus, the area of the square is 25 square cm, which can be written as 5 cm × 5 cm, that is, side ×  side.

From the above discussion, it can be inferred that the formula can give the area of a square is:

Area of a Square = Side × Side

Therefore, the area of square = Side²  square units

and the perimeter of a square = 4 ×  side units

Here some of the unit conversion lists are provided for reference. Some conversions of units:

• 1 m = 100 cm
• 1 sq. m = 10,000 sq. cm
• 1 km = 1000 m
• 1 sq. km = 1,000,000 sq. m

Area of a Square Sample Problems

Example 1:

Find the area of a square clipboard whose side measures 120 cm.

Solution:

Side of the clipboard = 120 cm = 1.2 m

Area of the clipboard = side  × side

= 120 cm × 120 cm

= 14400 sq. cm

= 1.44 sq. m

Example 2:

The side of a square wall is 75 m. What is the cost of painting it at the rate of Rs. 3 per sq. m?

Solution:

Side of the wall = 75 m

Area of the wall = side × side = 75 m × 75 m = 5,625 sq. m

For 1 sq. m, the cost of painting = Rs. 3

Thus, for 5,625 sq. m, the cost of painting = Rs. 3 × 5,625 = Rs 16,875

Example 3:

A courtyard’s floor which is 50 m long and 40 m wide is to be covered by square tiles. The side of each tile is 2 m. Find the number of tiles required to cover the floor.

Solution:

Length of the floor = 50 m

The breadth of the floor = 40 m

Area of the floor = length × breadth = 50 m × 40 m = 2000 sq. m

Side of one tile = 2 m

Area of one tile = side ×side = 2 m × 2 m = 4 sq. m

No. of tiles required = area of floor/area of a tile = 2000/4 = 500 tiles.

Practice Problems

1. A square wall of length 25 metres, has to be painted. If the cost of painting per square metre is ₹ 4.50. Find the cost of painting the whole wall.
2. Find the length of a square park whose area is 3600 square metres.
3. Find the area of the square whose length of the diagonal is 5√2 cm.

To learn and practice more problems related to the area of a square, download BYJU’S-The Learning App.