Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in.

Answer 1

Area of equilateral triangle is $12\sqrt{3}$$inch^{2}$.

Step-by-step explanation:

We have, 6 inch  apothem means height = 6 inch but we also know that height of an equilateral triangle is $\frac{\sqrt{3} }{2} a$.

∴ $\frac{\sqrt{3} }{2} a$ $= h$

⇒ $\frac{\sqrt{3} }{2} a$   $= 6$

⇒$a = 4\sqrt{3}$

Now, Area of equilateral triangle is  = $\frac{\sqrt{3} }{4} a^{2}$, putting value of a we get:

⇒ $\frac{\sqrt{3} }{4} (4\sqrt{3})^{2}$

⇒$\frac{\sqrt{3} }{4} (48)$

⇒$12\sqrt{3}$ $inch^{2}$

∴Area of equilateral triangle is $12\sqrt{3}$$inch^{2}$.