Answer:
C
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
The triangle is equilateral , since 3 angles = 60°
Then base AB = 12
Find height CD using the sine ratio in the right triangle ( there are 2 )
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{BC}[/tex] = [tex]\frac{CD}{12}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ← exact value of sin60° ( cross- multiply )
2CD = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
CD = 6[tex]\sqrt{3}[/tex]
Then
A = [tex]\frac{1}{2}[/tex] × 12 × 6[tex]\sqrt{3}[/tex] = 6 × 6[tex]\sqrt{3}[/tex] = 36[tex]\sqrt{3}[/tex] units² → C
