Question

Find the perimeter, apothem, and area of a regular triangle with a radius of 6sqrt3.

How do I do this?

Answer 1

Did you make a sketch of an equilateral triangle?

draw in the "centre", and the "radius", and the height (the apothem)
I see a right-angled triangle with a hypotenuse of
6√3, and angles 30° , 60° and 90°
label the base as x and the height of the right-angled triangle as y, and the height of the whole triangle as h
sin30 = y/6√3
y = (6√3)(1/2) = 3√3
cos30 = x/6√3
x = (6√3)(√3/2) = 9
also:
tan 60 = h/9
h = 9√3

side of the triangle = 2x = 18
perimeter = 3(18) = 54
area = (1/2)(2x)(h) = xh = 9(9√3) = 81√3