Area Of A Square - Introduction To Area

What is the Area of a Square?

Area of a square is defined as the number of square units needed to completely fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square meters (m2). For the computation of area, there are pre-defined formulas for squares, rectangles, circle, triangles, etc. In this article, you will learn about the area of a square.

Area of a Square Formula

Before getting to the area of square formula used for calculating the area, let us try using a 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 \(\times\) 1 cm squares. The square covers 25 complete squares.

Area Of A Square

Area of a Square

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 area of a square can be given by the formula:

Area of a Square = Side ×  Side

Therefore, the area of square = Side2  square units

and the perimeter of a square = 4 ×  sides 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 = 5625 sq. m

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

Thus, for 5625 sq. m, the cost of painting = 3  ×5625 = Rs 16875

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

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


Practise This Question

In the figure shown, dotted lines represent the heights to the corresponding bases BC,CA and AB respectively. Pick the figure which depicts the height incorrectly.