Quick Links
Quick Links
SAT
SAT Prep
Good SAT Score
1600 SAT Score 1590 SAT Score 1580 SAT Score 1570 SAT Score 1560 SAT Score 1550 SAT Score 1540 SAT Score 1530 SAT Score 1520 SAT Score 1510 SAT Score 1500 SAT Score 1490 SAT Score 1480 SAT Score 1470 SAT Score 1460 SAT Score 1450 SAT Score 1440 SAT Score 1430 SAT Score 1420 SAT Score 1410 SAT Score 1400 SAT Score 1390 SAT Score 1380 SAT Score 1370 SAT Score 1360 SAT Score 1350 SAT Score 1340 SAT Score 1330 SAT Score 1320 SAT Score 1310 SAT Score 1300 SAT Score 1290 SAT Score 1280 SAT Score 1270 SAT Score 1260 SAT Score 1250 SAT Score 1240 SAT Score 1230 SAT Score 1220 SAT Score 1210 SAT Score 1200 SAT Score 1190 SAT Score 1180 SAT Score 1170 SAT Score 1110 SAT Score 1100 SAT Score 1090 SAT Score 1080 SAT Score 1070 SAT Score 1060 SAT Score 1050 SAT Score 1040 SAT Score 1030 SAT Score 1020 SAT Score 1010 SAT Score 1000 SAT Score 990 SAT Score 980 SAT Score 970 SAT Score 960 SAT Score 950 SAT Score 940 SAT Score 930 SAT Score 920 SAT Score 910 SAT Score 900 SAT Score 890 SAT Score 880 SAT Score 850 SAT Score 840 SAT Score 830 SAT Score 820 SAT Score 810 SAT Score
Acceptance Rate
Math Prep
English Prep
ACT
ACT Scores Guide
SAT Tips
ACT Tips
College Guide
Home / Mathematics / Rhombus

Rhombus: Meaning, Properties, Area and Perimeter Formulas using Examples!

Last Updated on Mar 20, 2025
IMPORTANT LINKS
Geometry Percentage Linear Graphs Linear Equations Surface Area Logarithms Trigonometry System of Equations Complex Numbers Inequalities Complex Numbers Questions Surface Area and Volume Formulas Volume Quadratic Equation Coordinate Geometry Ratio and Proportion Linear Functions Compound Interest Hexagon Parallel Lines

What is a Rhombus?

A rhombus is a type of quadrilateral whose opposite sides are parallel and all four sides are equal in length. Moreover, it is also known as a diamond. It is a special case of parallelogram and kite in terms of sides and angles. If all the angles of the rhombus-shaped Geometric image are right angles then it is known as a square.

Check out the below image to understand the same.

Here you can check that, AB, BC, CD and AD are sides of the rhombus and the line joining AC represents the diagonal and the line joining BD denotes the diagonal of the rhombus.

Rhombus Formulas

As per the definition, we can say that every square is a rhombus but not all rhombuses are squares. Let us now learn the different formulas related to the topic.

Area of a Rhombus

We can define the area of a rhombus in maths as the amount of space covered by all four sides of a rhombus in a two-dimensional space. The area of the rhombus formula taking the diagonals, height and base as well as using trigonometric ratios are as follows.

The area of the rhombus using the diagonals:

If and , are the two diagonals then the area of the rhombus formula is equal to half of the product of the length of the diagonal. Mathematically this is written as: .

The area of the rhombus using height and base:

If we are given with the length of base and height (perpendicular distance from base to the opposite side of rhombus), then the area of rhombus = .

The area of the rhombus using side and trigonometric function:

In terms of a trigonometric function, we can say that the product of the square of the length of one side of the rhombus with the sine of any interior angle is equal to the area.

As per the property, ∠A = ∠C and ∠D = ∠B

The area of rhombus = .

For the above formula, a is the length of the side and A and B are the interior angle.

Perimeter of a Rhombus

Perimeter is the total length of boundaries or the total distance around the edges of a rhombus.

The perimeter of rhombus formula = 4a

As all the side of rhombus are equal i.e. AD = DC = CB = BA = a.

Properties of Rhombus

At this point of the article, we know the definition and different formula links with the area and perimeter. Let us now learn the important properties:

  • All the sides are of equal length.
  • Opposite sides are parallel to one another and the opposite angles are equal.
  • The summation of two adjacent angles is equivalent to 180 degrees.
  • The two diagonals bisect each other at right angles.
  • You will get a rectangle if you connect all 4 midpoints of the sides of the rhombus and the area of the rectangle will be half of the area of the rhombus.
  • If we connect the diagonals of the rhombus then they split the rhombus into four congruent triangles.
  • We can’t inscribe a rhombus in a circle. Similarly, we can’t circumscribe the circle around the rhombus.
  • A rhombus has 4 interior angles.
  • Adjacent angles of the rhombus are supplementary pairs.

Similarities between Squares and Rhombus

 

Throughout our discussion, we read the connection between squares and rhombuses. Let us understand the various similarities between these two shapes.

  • Both the square and rhombus are quadrilateral.
  • The diagonals of both square and rhombus bisect each other at right angles.
  • The opposite sides are parallel in both rhombus and square.
  • All the 4 sides of a rhombus as well as a square are of equal length.
  • The summation of all the interior angles of a square as well as a rhombus is equal to 360°.

Solved Examples of Rhombus

We have read all the details regarding the definition, formula and properties related to rhombus shaped objects. Let us now practise some solved examples.

Solved Example 1: Madhuri has a kite where the lengths of the two diagonals are 6 cm and 12 cm, respectively. Now she wants to colour the kite, then determine the area of the kite.

Solution:
Given:

Diagonal of the kites, = 12 cm, and = 6 cm

A = 36

The area of the rhombus shaped kite = 36 .

Solved Example 2: Determine the measure of the diagonal for a rhombus diagram, if the area is 169 and the longest diagonal is 26 cm long.

Solution: 

Given:

Area of rhombus diagram = 169 and let the longest diagram i.e. = 26 cm and the other diameter be denoted by .

Using area formula;

 

=13

Thus, the length of another diagonal is 13 cm.

Solved Example 3: What is the perimeter of a rhombus shape tile, when the measure of all sides is equivalent to 4.6 cm?

Solution:

The side of rhombus shape tile = 4.6 cm

According to the formula of;

Perimeter = 4 x side

P = 4 x 4.6

P = 18.4 cm

Conclusion

So, now you’ve got a solid grip on what a rhombus is all about! From its equal sides and special diagonals to formulas for area and perimeter—you’re all set to tackle those tricky geometry questions on exams like the SAT, ACT, PSAT/NMSQT, and more. Keep practicing, and spotting rhombuses (or diamonds!) in real life will feel just as easy as solving them on paper!

Report An Error