Question

in a regular hexagon with sides of 3inches is inscribed is a circle. find the area of the segment formed by a side of the hexagon and the circle.

the equation it goes to is in the comments

Answer 1

hey

Answer 2

\[A=(\frac{? }{ ? }\pi-\frac{ ? }{ ? }\sqrt{} ) inches ^{2}\]

Answer 3

The formula for the area of a triangle is A_tri = bh/2, where b is the length of the base (3"), and h is the height of the triangle, which must be found with trigonometry. For an equilateral triangle, h = bcos30°The area of one triangle is then A_tri = (1/2)(b^2)(cos30°) and the area of the hexagon is A_hex = (3b^2)(cos30°).

For a circle inscribed inside the hexagon, its radius is r = bcos30°, which you plug in to the formula for a circle's area A_cir = πr^2 to get A_cir = π(bcos30°)^2.

The area of one of the six segments outside the circle but inside the hexagon is

A_seg = (1/6)(A_hex - A_cir)

A_seg = (1/6)[(3b^2)(cos30°) - π(bcos30°)^2]

Plug in b = 3" and cos30° = 0.866 and the rest should be eas