Area of a Rhombus

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

The area of the rhombus can be written as the sum of the areas of △ ACD and △ ACB. These two triangles share the base AC and their heights are DE and BE, respectively. A &= A_(ACD) + A_(ACB) &⇓ A &= 1/2 AC* DE + 1/2 AC* BE Finally, use the fact that the heights of the triangles add up to d_1 and that the base is equal to d_2 to derive a formula for the area of a rhombus in terms of its diagonals.