Question

A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle. (Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.) No diagram.

Answer 1

now, based from the wording, I'd think what they want the Area including the arc,
or do they want the Area of just the Hexagon side only?

Answer 2

base on the given hint, the Area of the hexagon alone is just
$$
\cfrac{\sqrt{3}\times side^2}{4}\\
\text{now the circle's arc area is just}\\
\cfrac{180 \times radius^2}{2 \pi}
$$

Answer 3

so if i put it in \[A = ?/? \pi - ?/? \sqrt{?} form \] it would be 9/4 \[\sqrt{3}\] right? i now do not know how to find the first part of the equation. @jdoe0001

Answer 4

well, you see, I find the wording a bit ambiguous, it sounds like what's being asked is the Area of the Hexagon segment, not including the arc
so the 1st equation will do that

now if what's being asked is the Area of those 60 degrees in the circle, including the arc, then is the 2nd equation

Answer 5

i wish i knew if i could guess it would be the area of the ark
sorry for the bad drawling haha