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Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

6-inch apothem

A = sq. in

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A=√3/4 a²

a is the apothem and A is area:

A=√3/4(6)²

A= 9√3

Answer: 12√3 square inches

Step-by-step explanation:

By the property of equilateral triangle,

Apothem = √3/2 × Side

⇒ Side = 2/√3 × Apothem

Here, apothem = 6 inches

Thus, the side of the given equilateral triangle =  [tex]\frac{2}{\sqrt{3}}\times 6[/tex]

= [tex] \frac{12}{\sqrt{3}}[/tex]

= [tex]4\sqrt{3}[/tex]  unit

Since, For an equilateral triangle,

[tex]\text{ Area} = \frac{\sqrt{3}}{4}\times (\text{ side})^2[/tex]

⇒ The area of the given equilateral triangle = [tex] \frac{\sqrt{3}}{4}\times (4\sqrt{3})^2[/tex]

[tex]=\frac{\sqrt{3}}{4}\times 48[/tex]

[tex]=12\sqrt{3}[/tex]  square inches

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