Table of Contents

**What Is Rhombus**

Geometry has some type of shape. Especially in plane geometry, one type of quadrilateral is rhombus. Specifically, rhombus is special type of parallelogram that has four sides that has same length.

It is like square, but the angles in rhombus need not be right angles. Beside that it is also has diagonals that each of them bisects two opposite interior angles.

Another name of rhombus is “rhomb” or “diamond”. It is identic with in playing card. Rhombus is also used in many things in real life.

For example, it is applied in kite, windows, earing etc.

**Properties of Rhombus**

There are some properties of rhombus:

- All of side has same length
- The opposite sides are parallel
- The opposite angles are same.
- The diagonals bisect each other. It makes right angle.
- The diagonal bisects two opposite angles.

**Area of a Rhombus**

The area of a rhombus is an area that is bordered by four same sides that has same length. There are some formula or the area to each type of rhombus.

**Area is multiplication between height and the base.**

**A = height x base**

**A = h x b**

**Area is a half of multiplication between first and second diagonal.**

**A = (D**_{1}** x D**_{2}**) / 2**

**Area is multiplication between base square and sin of any angle.**

**A = s x h**

** = s x s.sin**α

** =s ^{2} x sinα**

**Perimeter of a Rhombus**

Perimeter means the sum all of rhombus’ sides. Let s as the length of side, then

**Perimeter = 4 x s**

**Examples**

- Given a rhombus KLMN that has LM = x+5, KL = 2x-9, then 2x = …?

Remember the properties that KL = LM.

Then,

2x – 9 = x + 5

2x – x = 5 + 9

x = 14

so, the value of 2x = 2.14 = 28.

2. Determine the ratio between area and perimeter of the rhombus.

- Area = h x b

= 8 x 9

= 72 cm^{2}

- Perimeter = 4 x 9 = 36 cm
- Ratio of area and perimeter = 72 : 36 = 2 : 1

3. Calculate the area.

a.

Calculating the area needs the height.

Using Pythagorean theorem, we get

h = √(17^{2} – 8^{2}) = √(289 – 64) = √225 = 15

then the area is:

A = h x b = 15 x 17 = 255

b.

First step is determining the length of diagonals.

Using Pythagorean theorem,

Let shortest diagonal is 2 x 6 = 12 cm

Then calculating for m

m = √(102 – 62) = √(100 – 36) = √64 = 8

so, longest diagonal is 2 x m = 2 x 8 = 16.

Consequently,

A = (D1 x D2) / 2

= (12 x 16) / 2

= 96