Question

if a circle has a radius of 6 inches,what will the area of the circumscribed equilateral triangle be?

Answer 1

Make a sketch
Draw a radius to each of the sides, it will meet it at right angles and bisect the sides
Draw lines from the centre to each of the vertices.
You should have 6 triangles with angles 30,60 and 90
one of the sides will be 6
I can find the other side of one of those triangles.
tan 30 = 6/x
1/√3 = 6/x
x = 6√3

so the area of one of those triangles = (1/2)(6√3)(6)
= 18√3

so the area of the whole big triangle is 6(18√3) = 108√3