Area of a square is the amount of surface that is enclosed in between the boundaries of a square. A square is any special rectangle with all four sides being equal. The diagonals of a square are equal and bisect each other at right angles. Its diagonals also bisect each of the opposite angles. On this page, we will discuss the area of a square in detail.
What is an area of a square?
The area of a square is the amount of surface enclosed by its boundaries. Since the square is a special rectangle and we know the area of a rectangle is Length × width. Hence the formula for finding a square is L × W. But in a square all four sides are equal. This shows that area of a square = length × length = L × L = L².
How to find the area of a square.
In finding the area of a square, we take the square of the length of one side i.e (Length)² = L². Since all the sides of a square are equal. Before going straight to find the square of one side, make sure the unit of measurement is the same. When a question is given in one unit and you are asked to find the area in another unit. Convert the unit to the required unit and proceed with finding the area. Let’s look at some examples of the area of a square.
Example 1. Find the area of the square with a side of 7cm. Solution
The formula for the area of square = length × length = L², length = 7cm
= 7cm × 7cm = 7²
Example 2. Find the area of the square with a side of 8cm
The formula for finding the area of a square = (length)² = L², where length = 8cm
= 8cm × 8cm
At times you will be given the area of a square and you are asked to find the length of its side, in this case since the area of a square = L², where the L= length of one side of the square, we square root both side of the equation to make the length stand alone. Let’s understand this more with examples.
Example 1. If the area of the square is 81cm². Find the length of its sides.
The formula for finding the area of a square = (length)² where the area of the square = 81cm², length =?
81cm² = L²
square root both sides of the equation = √81 = √L²
9cm = L
Therefore, the length of one side of the square is 9cm.
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