Take a rectangular squared paper and make a rhombus as shown in the figure.
Here, Draw a diagonal BD. Now, the rhombus you made is divided into two triangles.
Hence, the area of rhombus = Area of ΔABD + Area of ΔCBD
= ½ × d₂ × (OA) + ½ × d₂ × (OC)
= ½ × d₂ × (OA + OC)
= ½ × BD × AC = ½ × d₁ × d₂