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 a rhombus = Area of triangle 1 + Area of triangle 2
= 
+
= 
Using the above we can write the area of a rhombus to be equal to half the product of its two diagonals.
Example 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.
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
= 
+
= 28 + 28
= 56 cm2
Using the formula, we get the area of a rhombus : A = 
xy
= x 14 x 8
= 56 cm2
Example 2 : What is the area of the rhombus in this diagram.
Splitting the rhombus along the longer diagonal gives two triangles.
Area of rhombus = area of triangle 1 + area of triangle 2
= 
+
= 77 + 77
= 154 cm2
Applying the formula, we get the area of the rhombus: A = xy
= x 22 x 14
= 154 cm2