Question

Find the area of an equilateral triangle with radius 5√3 m. Leave your answer in simplest radical form.

Answer 1

`(225)/(4)`
`√(3)`
`m^(2)`

Answer 2

In an equilateral triangle the radius of inscribed circle is equal to

`r= (a √(3) )/(6)`, so

`5 √(3) = (a √(3) )/(6)` and

`a=30`.
The area of this equilateral triangle is
`A= (a^2 √(3) )/(4) =(30^2\cdot √(3) )/(4)=225 √(3)` square units.