#1**+1 **

Note....that the diagonals of a rhombus are perpendicular.....they form a 90 degree angle

So...triangle CEB is a 30-60-90 right triangle

The hypotenuse of this triangle is 12

Angle ECB = 30 degrees.....and the side opposite this angle = 1/2 of the hypotenuse = 6

So EB = 6......and since the diagonals bisect each other....then DB = 12

Also..in triangle CEB....the side opposite the 60 degree angle = √3 times the side opposite the 30 degree angle = 6√3

So.....CE = 6√3 and CA = 2 * 6√3 = 12√3

So...the area = (1/2) product of the diagonal lengths =

(1/2) (12) (12√3) =

72√3 units^2

CPhill
May 2, 2018