Answer:
Area = 11.66 square inches .
Step-by-step 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 : [tex]R = \frac{\sqrt{3}\ side}{3}[/tex].
Plug the value of radius = 3 inches .
[tex] 3 = \frac{\sqrt{3}\ side}{3}[/tex].
On multiplying both sides by 3.
[tex]9 = \sqrt{3}\side[/tex].
On Dividing both sides by root 3 both sides .
[tex]\frac{9}{\sqrt{3}} = side[/tex] .
Side = 5. 19.
Area of equilateral triangle : [tex]\frac{\sqrt{3}\ side^{2}}{4}[/tex].
Plug side = 5.19
Area of equilateral triangle : [tex]\frac{\sqrt{3}\ (5.19)^{2}}{4}[/tex].
Area = 11.66 square inches .
Therefore, Area = 11.66 square inches .
