Question

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

6-inch apothem

A = sq. in

Answer 1

A=√3/4 a²

a is the apothem and A is area:

A=√3/4(6)²

A= 9√3

Answer 2

Answer: 12√3 square inches

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 =
`(2)/(√(3))* 6`

=
`(12)/(√(3))`

=
`4√(3)` unit

Since, For an equilateral triangle,

`\text{ Area} = (√(3))/(4)* (\text{ side})^2`

⇒ The area of the given equilateral triangle =
`(√(3))/(4)* (4√(3))^2`

`=(√(3))/(4)* 48`

`=12√(3)` square inches