## Rhombus

Rhombus is a 2-D plane figure with a closed shape.

All sides of a rhombus are equal.

Rhombus is a type of parallelogram.

A rhombus can also known as diamond, rhomb, and lozenge.

## Area of Rhombus

In fig., ABCD is a rhombus and AC and BD are its diagonals.

Diagonal BD divides the rhombus ABCD into two congruent triangles DCB and DAB.

Area of ABCD = Area of triangle DCB + Area of triangle DAB

= 1\2 x DB x OC + 1\2 x DB x OA

= 1\2 x DB x (OC + OA)

= 1\2 x DB x AC

## Rhombus formula

We can find the area of the rhombus in many ways, which is given below.

**1. Area of Rhombus using height and Base**

When the height h and the length of the sides b, the area of a rhombus is given by the formula;

Area of rhombus = base × height

**A = b × h**

### 2. Area of Rhombus Using Diagonals

Area of Rhombus = ½ × d1 × d2

Where d1 and d2 are the diagonals of a rhombus.

### 3. Area of Rhombus using the Length of the Sides and Angle.

The area of a rhombus is equal to the multiple side length squared and the sine of the angle between the two sides.

**Area of rhombus = b**^{2} × Sine (A)

^{2}× Sine (A)

Where A = angle formed between two sides of a rhombus

## Find the area of a rhombus!!

*Example 1*

**Find the area of a rhombus whose side is 40 cm and height is 25 cm.**

__Solution__

As we know the area of a rhombus A = b × h

= (40 x 25) cm^{2}

= 1000 cm^{2}

*Example 2*

**If the height and area of a rhombus are 9 cm and 54 cm ^{2,} respectively, find the rhombus’s dimensions.**

__Solution__

A = b × h

54 cm^{2} = 8 cm x b

Divide both sides by 8.

54 cm^{2}/9 cm = b

b = 6 cm.

Therefore, the dimensions of the rhombus are 6 cm by 6 cm.

*Example 3*

**The two diagonals of a rhombus are 10 cm and 12 cm. find the rhombus area.**

**Solution**:

Let d_{1} = 10 cm and d_{2} = 12 cm.

A = ½ × d_{1} × d_{2}

= (½ × 10 × 12) cm^{2}.

= 60 cm^{2}.

*Example 4*

**Find the area of a rhombus whose sides are 7 cm, and the angle between the two sides is 90 degrees.**

__Solution__

Area of a rhombus = b^{2} × Sine (A)

= 7^{2} x sine (60)

= 49 cm^{2}.