Rhombus

Rhombus is a type of figure which only has 2 dimensions. It is a plane figure. It has certain unique properties which makes it a special form of a parallelogram. Rhombus also has an identity that is pretty unique as a figure that is quadrilateral. Rhombus is also called at times equilateral quadrilateral. It is so-called because the sides of a rhombus have the same length. A square can be defined as a rhombus but all rhombus need not have right angles. For that reason, when they are at right angles in a rhombus then it could be called a square. 

Rhombus

Rhombus is a shape where diagonals bisect the figure into lengths that are equal. These bisections occur at a right angle. The resultant sum of the angles will always be 180 degrees. In Quantitative Aptitude, questions relating to the area, its formulae, its differences with square, and problems based on volume as well as the surface area might come. For that reason, the following solutions will contain those explanations. The area of a rhombus can be found by calculating the sum of the diagonal lengths and then multiplying it by half. It has a convex polygon and can be classified as an isogonal figure.

Rhombus Parallelogram

Rhombus and parallelogram have certain similarities. Both of them are polygons having four sides and are known as quadrilaterals. But they have certain key differences. Those differences have been provided as follows:

Table 1 shows differences between a rhombus and a parallelogram

Rhombuses can thus be said to be special cases of a rhombus parallelogram. Rhombus parallelogram also has a special superellipse. It only has an exponent of 1. It is represented as (±a, 0) and (0, ±b). This is known as the cartesian equation. 

Rhombus Square

Rhombus and square share many similarities as well. A square can be defined as a rhombus but all rhombus need not have right angles. For that reason, when they are right angles in a rhombus then it could be called a square. There are certain differences between square and rhombus which are provided below:

Table 2 shows differences of Rhombus and Square

While all squares can be rhombuses, not all rhombuses are squares. 

Rhombus Problem

 Given below are some rhombus problems:

1. If there is a perimeter that is 120 feet of a given rhombus and the diagonal length is 40 feet what will be its area?

Solution: Given that all sides of a rhombus are the same when a perimeter of 120 feet is given then, 

• 120/4 = 30

Then, CB=30 feet

• Then CO side of the triangle at the right = ½ of diagonal

Which are 20 feet.

So, OC=20 feet

• Applying Pythagoras’ Theorem,

CB2=OB2+CO2

So, 302=OB2+202

Then, OB is the square root of 5

• So, the area= 400 square root of 5 ft2

Properties of Rhombus

Here are some properties of the rhombus:

• Every side is equal
• Opposite angles are equal
• Sum of adjacent angles in a rhombus is 180 degrees
• Symmetry can be found in two lines
• No circumscribing circle can be drawn
• Bisecting diagonal at angles

Conclusion

Therefore, studying the rhombus and its various aspects is important so that problems could be solved accurately. It is for this reason that the article has looked at the properties of the rhombus, how it is similar and dissimilar to squares and parallelograms. Rhombus can also be compared with trapezium. The article has also looked at how the area of a rhombus can be solved. It has also provided certain differences between parallelogram and square with rhombus.