[tex]\bold{METHOD\ 1:}\\\\\text{We have four right triangles with legs}\ a=4\sqrt3\ m,\ b=4m.\\\\\text{The formula of an area of a right triangle}:\\\\A=\dfrac{ab}{2}\\\\\text{Substitute:}\\\\A_\triangle=\dfrac{(4\sqrt3)(4)}{2}=\dfrac{16\sqrt3}{2}=8\sqrt3\ m^2\\\\\text{The area of the rhombus}\\\\A=4A_\triangle\to A=(4)(8\sqrt3)=32\sqrt3\ m^2[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{The formula of an area of a rhombus:}\\\\A=\dfrac{ef}{2}\\\\e,\ f-\text{diagonals}\\\\\text{We have}\\\\e=(2)(4)=8\ m\\f=(2)(4\sqrt3)=8\sqrt3\ m\\\\\text{Substitute:}\\\\A=\dfrac{(8)(8\sqrt3)}{2}=\dfrac{64\sqrt3}{2}=32\sqrt3\ m^2[/tex]
