Properties of Square

by Anshu Dev
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A two-dimensional shape that is regarded as a regular quadrilateral is known as a square. It is composed of four sides and angles. These angles are equivalent to the measure of 90 degrees. Hence, the total sum of the angles of the square is 360 degrees. The four sides of a square are opposite and parallel to each other respectively. Square is a type of quadrilateral, thus it consists of various similar properties to that of the rectangle and other two-dimensional shapes. However, let us discuss the properties of the square.

  1.  A quadrilateral with four vertices and four sides is a square.
  2.  The four sides of a square are congruent or equal to each other.
  3.  As mentioned, a square is composed of four sides, the opposite sides of a square are parallel to each other. Let us assume ABCD is a square where AB, BC, CD, and DA are its sides. Then, the parallel sides are DA and BC.
  4.  A square is made up of 4 angles. Each angle measures 90 degrees. Hence, the sum of the interior angles of a square is equivalent to 360 degrees.
  5.  We already discussed that the sides of a square are parallel to each other. In this case, a square is also known as a parallelogram.
  6.  The diagonals of a square are equal in measurement or length.

Rectangle

In mathematics, there are various types of geometrical shapes used to understand and visualize various mathematical concepts. One of them is therectangle. A rectangle is also regarded as a quadrilateral, thus it is a 2-dimensional figure.
Hint: A figure which comprises only length and width or breadth is known as a two-dimensional figure. Its longer side is considered as length and the shorter length as the breadth or width. Let us now discuss the properties of a rectangle:

  1. A rectangle is made up of four sides. The opposite sides of the rectangle are parallel or congruent to each other. Hence, it is also known as a quadrilateral.
  2.  It is made up of 4 angles. Each angle measures 90 degrees. Thus, the sum of all the interior angles is equivalent to 360 degrees.
  3.  However, you must not consider that all the parallelograms are rectangles. A rectangle can be parallelogram always, but a parallelogram cannot be always considered a rectangle.
  4.  The area of a rectangle is the resultant value of the multiplication of width and breadth. Mathematically, the area of the rectangle = l * b.

Examples

To recall, the formula for the area of a rectangle is given as the length * breadth or l * b. Some examples are based on the area of a rectangle.

Example 1:Find the area of the rectangle, if the measurement of the length and breadth is 4 cm 8 cm respectively.
Solution:

                  Given,

                  Length of the rectangle = 4 cm

     Breadth = 8 cm

                  Using the formula = l * b,

                  4 cm * 8 cm = 32 cm square units.

                  Hence, the area of the rectangle is 32 cm square units.

Example 2: Find the area of the rectangle, if the measurement of the length and breadth is 6 cm 4 cm respectively.
Solution:

                   Given,

                   Length of the rectangle = 6 cm

                   Breadth = 4 cm

                   Using the formula = l * b,

                  6 cm * 4 cm = 24 cm square units.

                  Hence, the area of the rectangle is 24 cm square units.

For more problems on the area of a rectangle and the properties of a square, learn from the Cuemath experts. 

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