What is a Square?
A square is a quadrilateral in which the opposite sides are parallel and another feature is that all the four sides are equal in length. We also observe from the image that all the four interior angles of a square measure 90°. Moving on to the diagonals, every square has equal diagonals, with them bisecting each other at right angles.
To make things interesting, based on the image of a square can you name a few square shaped objects you come across daily?
A few objects such as paper napkins, chess boards, a slice of bread or even a pizza box, are in the shape of a square.
What is the Area of a Square?
The area of a square is defined as the measure of the region occupied by the square. If the side of the square is ‘s’ then the area can be determined by the equation,
Area of square, \(A = s^{2}\)
Units to measure the Side of a Square
Common units to measure distance are used to measure the side of a square. We can start with large units like miles, move on to smaller units like yards, feet, inches, centimeters and even millimeters.
Units to measure the Area of a Square
As the area of closed geometric shapes such as a square is always measured in square units, similarly we use units such as square millimeters, square centimeters, square meters, square inches, square feet, square yards and square miles.
Solved Examples
Example 1: Find the area of a square with one its sides measuring 8 inches.
Solution:
As stated,
Side of the square = 8 in
\(A= s^{2}\) [Formula for area of square]
\(=8^{2}\) [Substitute 8 for ‘s’]
\(=\text{ }64\text{ }sq.\text{ }in. \) [Simplify]
So, the area of the square is 64 square inches.
Example 2: What is the area of the square in the image?
Solution:
As stated,
Side of the square = 9 ft
\(A = s^{2} \) [Formula for area of square]
\(=9^{2} \) [Substitute 9 for s]
\(= 18\text{ }sq.\text{ }ft.\) [Simplify]
Hence, the area of the square is 81 square feet.
Example 3: William owns a square shaped agricultural field with an area of 1936 square meters. What is the side length of this field?
Solution:
As stated,
Area of the agricultural field = 1936 sq.m
\(A = s^{2}\) [Formula for area of square]
\(1936 = s^{2}\) [Substitute 1936 for A]
\(\sqrt{1936} = \sqrt{s^{2}}\) [Apply square root to each side]
\(44 = s\) [Simplify]
\(s = 44\) [Rewrite the above equation]
So, the side of the field is 44 meters.
There are four equal angles that are 90°.
The key difference between a square and a rectangle is that all the sides of a square are equal in length, but in a rectangle, it’s just the opposite sides that are equal in length.
The measure of total length of the boundary of a square is known as the perimeter. It’s quite simple to find the perimeter of a square, it’s to add up the lengths of its sides, or, it is 4 times the length of one side.
Perimeter is a measure of length, so all the units of length are used as units to express perimeter.