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Area of a Rhombus

A rhombus is like a parallelogram but with all its sides of equal length. The area of a rhombus can be found by dividing the figure into two equal triangles along one of its diagonals.

area of rhombus_1

Area of a rhombus = Area of triangle 1 + Area of triangle 2

= 1/2~x(y/2) + 1/2~x(y/2)

= {1/2}xy

Using the above we can write the area of a rhombus to be equal to half the product of its two diagonals.

 

area of rhombus_2Example 1 : Calculate the area of this rhombus.

 

Let us calculate the area of this rhombus through the two approaches – by splitting the rhombus into two triangles, and by using the formula.

area of rhombus_3

Since the diagonals are perpendicular to each other, they bisect each other to form equal parts of the respective diagonals. So the heights of the two triangles are 4 cm each (half of 8 cm).

Area of a rhombus = area of triangle 1 + area of triangle 2

= (1/2~*~14~*~4) + (1/2~*~14~*~4)

= 28 + 28

= 56 cm2

Using the formula, we get the area of a rhombus : A = 1/2 xy

1/2 x 14 x 8

= 56 cm2

 

area of rhombus_4Example 2 : What is the area of the rhombus in this diagram.

 

Splitting the rhombus along the longer diagonal gives two triangles.

area of rhombus_5

Area of rhombus = area of triangle 1 + area of triangle 2

= (1/2~*~22~*~7)(1/2~*~22~*~7)

= 77 + 77

= 154 cm2

Applying the formula, we get the area of the rhombus: A = 1/2xy

1/2 x 22 x 14

= 154 cm2