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Area of Rhombus – Formula and Examples


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.

Rhombus

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;

Rhombus formula

Area of rhombus = base × height

A = b × h

2. Area of Rhombus Using Diagonals

Area-of-Rhombus-Using-Diagonals

Area of Rhombus = ½ × d1 × d2

Where d1 and d2 are the diagonals of a rhombus.

area 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-using-the-Length-of-the-Sides-and-an-included-Angle

Area of rhombus = b2  × 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) cm2

= 1000 cm2

Example 2

If the height and area of a rhombus are 9 cm and 54 cm2, respectively, find the rhombus’s dimensions.

Solution

A = b × h

54 cm2 = 8 cm x b

Divide both sides by 8.

54 cm2/9 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 d1 = 10 cm and d2 = 12 cm.

A = ½ × d1 × d2

= (½ × 10 × 12) cm2.

= 60 cm2.

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 = b2 × Sine (A)

= 72 x sine (60)

= 49 cm2.