Area Of A Square - Introduction To Area

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.

What is the Area of a Square?

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 \(\times\) 5 cm, that is, side x 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 \(\times\) Side

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

Examples and Problem Statements

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 \(\times\) side = 120 cm \(\times\) 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 \(\times\) side = 75 m \(\times\) 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 \(\times\) 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

Breadth of the floor = 40 m

Area of the floor = length \(\times\) breadth = 50 m \(\times\) 40 m = 2000 sq. m

Side of one tile = 2 m

Area of one tile = side \(\times\) side = 2 m \(\times\) 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 area of a square, download BYJU’S-The Learning App.


Practise This Question

If AD||BC, then area (ΔABC) = area (ΔBEC). = area (ΔDBC) Say true or false