Areas of Parallelograms, Triangles, and Trapezoids
Rule

Area of a Rhombus

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

Alternatively, since a rhombus is a parallelogram, its area can also be calculated by multiplying its base and height.

Rhombus

Proof

Consider a rhombus and draw its two diagonals. Recall that the diagonals bisect each other at a right angle. Let be the point of intersection between the diagonals.

Rhombus and diagonals
The area of the rhombus can be written as the sum of the areas of and These two triangles share the base and their heights are and respectively.
Finally, use the fact that the heights of the triangles add up to and that the base is equal to to derive a formula for the area of a rhombus in terms of its diagonals.
Simplify
Exercises