Area of equilateral triangle is [tex]12\sqrt{3}[/tex][tex]inch^{2}[/tex].
Step-by-step explanation:
We have, 6 inch apothem means height = 6 inch but we also know that height of an equilateral triangle is [tex]\frac{\sqrt{3} }{2} a[/tex].
∴ [tex]\frac{\sqrt{3} }{2} a[/tex] [tex]= h[/tex]
⇒ [tex]\frac{\sqrt{3} }{2} a[/tex] [tex]= 6[/tex]
⇒[tex]a = 4\sqrt{3}[/tex]
Now, Area of equilateral triangle is = [tex]\frac{\sqrt{3} }{4} a^{2}[/tex], putting value of a we get:
⇒ [tex]\frac{\sqrt{3} }{4} (4\sqrt{3})^{2}[/tex]
⇒[tex]\frac{\sqrt{3} }{4} (48)[/tex]
⇒[tex]12\sqrt{3}[/tex] [tex]inch^{2}[/tex]
∴Area of equilateral triangle is [tex]12\sqrt{3}[/tex][tex]inch^{2}[/tex].