Is Square a Rhombus
Introduction
A laptop screen, blackboard, kite, etc., are all quadrilaterals. A quadrilateral is a four-sided polygon. The term quadrilateral is an amalgamation of two words: quad, meaning four, and lateral, meaning side.
They are given specific names depending on whether they are parallel, equal angles, or equal sides:
- A Rectangle is said to be a quadrilateral as all the four angles are equal to 90°.
- A Square is also a quadrilateral as all the four sides of a square and all the angles are same.
- A Rhombus is a quadrilateral where the length of all its sides is same.
- In addition to the classification of quadrilaterals depending on their sides and angle, specific names are given depending on whether or not opposite sides are parallel
- If one pair of sides is parallel, the quadrilateral is called a Trapezoid. When both sides are parallel, it is called a Parallelogram.
Square
Since a square has four sides it is called quadrilateral. Squares are quadrilateral which has equal sides and equal angles.
Properties of a square
- All four sides of a square are same and equal.
- It has same opposite sides.
- Opposite sides of a square are parallel.
- The angles inside the square (or interior angles) are all 90° and are equal. Thus, the sum of all the angles is 360, i.e., 90*4=360°.
- It has equal opposite angles.
- The sum of the two adjacent angles is 180°.
- It has 4 lines of symmetry.
- We get the same square if a square is rotated counter clockwise at 90°. Thus, the rotational symmetry of a square is 4
- Diagonals intersect each other at 90° or, in other words, perpendicularly. When they intersect, the portions are equal.
Area of a Square
A square is generally the area enclosed inside the figure. In this context, let us name each side of the square as ‘l’, then the area of a square is given by l*l which is l2
The perimeter of a Square
The perimeter is the sum of four sides of a square. If we name each side of a square as ‘l’, then the perimeter = l+l+l+l = 4l
Rhombus
A rhombus is a quadrilateral with four equal sides.
Properties of a Rhombus
- All four sides of a rhombus are equal.
- Opposite sides are same.
- Has parallel opposite sides.
- Interior angles are not equal; however, the sum of all the interior angles is 360°. It has equal pair of acute angles and an equal pair of obtuse angles.
- The opposite angles are not 90°but are equal. A pair of obtuse angle and a pair of acute angle make the opposite angles.
- The sum of adjacent angles is 180°.
- It has two lines of symmetry.
- The rotational symmetry is two.
- Diagonals intersect each other perpendicularly.
Area of a Rhombus
If we consider the length of the diagonals of a rhombus as l1 and l2, then the area of a rhombus is (l1*l2)/2
The Perimeter of a Rhombus
If we consider the side of a rhombus as ‘l’, then the perimeter of a rhombus is 4l
Is Square a Rhombus?
Though both rhombus and square are quadrilaterals, they differ in aspects like the length of their sides, diagonals, and shape.
They differ in:
- Firstly, a rhombus has equal opposite angles where one pair is acute, and the other is obtuse. Whereas, in a square, all the angles are equal and are equal to 90°
- Secondly, the length of a diagonal in a square is equal, whereas, in a rhombus, they are not equal.
- With this, we can say a square is a rhombus, and the other way is not true.
- A square can be considered a rhombus since the length of every side of a square is equal. The diagonals of a rhombus and a square intersect perpendicularly.
Examples
1. Find the area and the perimeter of a square pool with each side 200m.
Solution:
Given: length of a side of a pool: 200m
We know that,
Area of a square= l2
= 200*200= 40000m
The Perimeter of a square= 4*l
= 4*200= 800m
2. Find the perimeter of a rhombus of side 400m
Solution:
Given: length of each side: 400m
The Perimeter of a rhombus= 4*l
= 4*400= 1600m