Question

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

3-inch radius
A = sq. in.

Answer 1

Your answer is 11.664, which is very nearly 27/4 sqrt(3)

Answer 2

Area = 11.66 square inches .

Explanation:

Given : An equilateral triangle (regular 3-gon) with the given measurement.

3-inch radius.

To find : Find the area .

Solution : We have given that

Radius = 3 inches.

By the formula :
`R = (√(3)\ side)/(3)`.

Plug the value of radius = 3 inches .

`3 = (√(3)\ side)/(3)`.

On multiplying both sides by 3.

`9 = √(3)\side`.

On Dividing both sides by root 3 both sides .

`(9)/(√(3)) = side` .

Side = 5. 19.

Area of equilateral triangle :
`(√(3)\ side^(2))/(4)`.

Plug side = 5.19

Area of equilateral triangle :
`(√(3)\ (5.19)^(2))/(4)`.

Area = 11.66 square inches .

Therefore, Area = 11.66 square inches .