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.
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.
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?
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.
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.