Question

A regular hexagon is drawn so that one of its sides is the longest chord of a circle. If the figure formed by connecting every other vertex of the hexagon has a perimeter of 9, what is the area enclosed by the circle?

Answer 1

\[P=6\times\text {side}\]

Answer 2

find the side length and hence the diameter, then find the area of the circle

Answer 3

is it 3π/4?

Answer 4

Yeah. I figured out it's a 30-60-90 triangle and gets the diameter to be √3?

Answer 5

you know the internal angle in a hexagon/?

Answer 6

yeah good

Answer 7

Then (√3/2)^2π = 3π/4?

Answer 8

How did you find the side