Answer:
72[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ (d₁ and d₂ are the diagonals )
The diagonals bisect each other at right angles
d₁ = 2 × 6 = 12
Use the tangent ration in the upper left right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex]
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{opp}{6}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 6 )
opp = 6[tex]\sqrt{3}[/tex] , then
d₂ = 2 × 6[tex]\sqrt{3}[/tex] = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex]