Question 189851
One of the formulas for the area of a rhombus is {{{A=s^2*sin(x)}}} where "s" is the length of the side and "x" is the angle given



{{{A=s^2*sin(x)}}} Start with the given formula



{{{A=12^2*sin(60)}}} Plug in {{{s=12}}} and {{{x=60}}}



{{{A=144*sin(60)}}} Square 12 to get 144



{{{A=144*(sqrt(3)/2)}}} Evaluate the sine of 60 to get {{{sqrt(3)/2}}} (use the unit circle)



{{{A=(144*sqrt(3))/2}}} Multiply



{{{A=72*sqrt(3)}}} Reduce



*[Tex \LARGE A \approx 124.708] ... Approximate the right side using a calculator



So the area of the rhombus is about 124.708 square mm.