# 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.

## Practice Problems

Problem 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.

Formula for area of a rhombus :

=   1/2 ⋅ (d1d2)

Substitute 24 for d1 and 15 for d2.

=   1/2 ⋅ (24 ⋅ 15)

=   12 ⋅ 15

=  180 in2

So, Cedric needs 180 square inches of fabric to make the kite.

Problem 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 :

Formula for area of a rhombus :

=   1/2 ⋅ (d1d2)

Substitute 25 for d1 and 15 for d2.

=   1/2 ⋅ (25 ⋅ 15)

=   1/2 ⋅ (375)

=  187.5 in2

Problem 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 :

Formula for area of a rhombus :

=   1/2 ⋅ (d1d2)

Substitute 12 for d1 and 16 for d2.

=   1/2 ⋅ (12 ⋅ 16)

=   6 ⋅ 16

=  96 in2

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

Area of parallelogram  =  96 in

base x height  =  96

Substitute 10 for base.

10 x h  =  96

Divide each side by 10.

height  =  9.6 inches

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