The Perimeter of a shape is the total distance around it. When it comes to a Rhombus all four sides are equal in length. Therefore, the Perimeter of a Rhombus can be acquired by adding all 4 sides or simply multiplying a side into four. Read on to learn more about the Perimeter of a Rhombus, the Formula to find the Perimeter of a Rhombus when the Sides and Diagonals are given in the question and Examples of the same.
What is a Rhombus?
A Rhombus is a four-sided shape which is also called a quadrilateral where all four sides have the same length. Imagine the shape of a Diamond.
Furthermore, here are Points to Remember about a Rhombus:
- All sides of a Rhombus have equal lengths.
- Corresponding angles located on opposite sides are of equal measure.
- The opposite sides run parallel to each other.
- The total sum of any two neighbouring angles equals 180 degrees.
- Each diagonal divides the vertex angles into two equal parts.
- The diagonals intersect each other at right angles, hence dividing each other into equal parts.
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Perimeter of a Rhombus Formula when Sides are given
When the Sides of a Rhombus are given, the Formula is simple. As you are already aware the sides of a Rhombus are equal. Hence, to find out the Perimeter of a Rhombus you need to add up all the sides.
Perimeter = a + a + a + a
Or
Perimeter = 4 a (which means a is multiplied 4 times)
For Example, if the side given is 4 meters. Thus, the Perimeter shall be:
Perimeter = 4 + 4 + 4 + 4 = 16
Or
Perimeter = 4 ✕ 4 = 16
Therefore, the Perimeter of a Rhombus whose side is 4 meters is 16.
Also Read: Perfect Squares: Concepts, Properties & GMAT Questions
Perimeter of a Rhombus Formula when Diagonals are given
A Rhombus has two diagonals that intersect with each other at Right angles = 90 degrees. Additionally, these Diagonals split the Rhombus into four right-angled triangles. The Diagonals of a Rhombus also bisect each other which means that they cut each other in half.
Things to keep in mind:
- When the Diagonals intersect, they create right-angled triangles inside the Rhombus.
- Moreover, each side of the Rhombus is the hypotenuse of these right-angled triangles.
- To find the side length of the Rhombus, you will need to use the Pythagorean theorem (a2 + b2 = c2) in one of these right-angled triangles.
To keep it simple, follow these steps along with the examples:
- Find the lengths of the diagonals.
- Suppose the lengths of the diagonals are 5 and 10.
- Square both lengths and add them together.
- 52 = 25
- 102 = 100
25 + 100 = 125
- Take the Square root of that sum.
- Square Root of 125 = 11.18
- Multiply by 2 to get the Perimeter.
- 11.18 ✕ 2 = 22.36
Thus, the Perimeter of the Diagonals 5 and 10 is 22.36
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What is the Perimeter of Rhombus with Diagonals 10 and 24?
The Perimeter of Rhombus with Diagonals 10 and 24 is as follows:
10 = 102 = 100
24 = 242 = 576
100 + 576 = 676
The Square root of 676 = 26
26 ✕ 2 = 52
Thus, the Perimeter of Rhombus with Diagonals 10 and 24 is 52.
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