# FINDING THE AREA OF A RHOMBUS

## About "Finding the area of a rhombus"

Finding the area of a rhombus :

The area of a rhombus is half of the product of the lengths of its diagonals.

## Relationship between rhombus and rectangle

A rhombus is a quadrilateral in which all sides are congruent and opposite sides are parallel. A rhombus can be divided into four right triangles that can then be rearranged into a rectangle.

The base of the rectangle is the same length as one of the diagonals of the rhombus. The height of the rectangle is half the length of the other diagonal.

## Finding the area of a rhombus - Examples

Example 1 :

Cedric is constructing a kite in the shape of a rhombus.The spars of the kite measure 15 inches and 24 inches. How much fabric will Cedric need for the kite?

Solution :

To determine the amount of fabric needed, find the area of the kite.

Area of rhombus  =  (1/2) x (d₁ x d₂)

here, d₁ = 24 in and d₂ = 15 in

=  (1/2) x 24 x 15

=  12 x 15

=  180 square inches

Hence, 180 square inches of fabric are needed to  Cedric to make the kite.

Example 2 :

A kite in the shape of a rhombus has diagonals that are 25 inches long and 15 inches long. What is the area of the kite?

Solution :

Area of rhombus  =  (1/2) x (d₁ x d₂)

here, d₁ = 25 in and d₂ = 15 in

=  (1/2) x 25 x 15

=  187.5 square inches

Example 3 :

The diagonals of a rhombus are 12 in. and 16 in. long. The length of a side of the rhombus is 10 in. What is the height of the rhombus?

Solution :

Area of rhombus  =  (1/2) x (d₁ x d₂)

here d₁ = 12 inches and d₂ = 16 inches

=  (1/2) x 12 x 16

=  96 square inches

Since a rhombus is a parallelogram, we can use the formula for the area of a parallelogram to find the height of the rhombus.

Area of parallelogram = 96

base x height = 96

10 x h = 96

h = 96/10 = 9.6 inches

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