Answer:
The area of an equilateral triangle is \(83.13m^2\).
Step-by-step explanation:
Given: The radius of an equilateral triangle is 8m.
To find: The area of an equilateral triangle.
Solution: It is given that the radius of an equilateral triangle is 8m.
Now, height of the triangle is given as:
\(h=2r\)
Substituting the value of r, we have
\(h=2(8)\)
\(h=16m\)
The side of the triangle is given as:
\(a=hsin(60^{\circ})\)
\(a=16(sin60^{\circ})\)
\(a=16(\frac{\sqrt{3}}{2})\)
\(a=8\sqrt{3}m\)
Now, the area of an equilateral triangle is given as:
\(Area=\frac{\sqrt{3}}{4}(a^2)\)
\(Area=\frac{\sqrt{3}}{4}(8\sqrt{3})^2\)
\(Area=\frac{\sqrt{3}}{4}{\times}64{\times}3\)
\(Arae=48\sqrt{3}m^2\)
\(Area=83.13m^2\)
Therefore, the area of an equilateral triangle is \(83.13m^2\).
