Trig problem using the area of a sector.?
A hexagon is inscribed in a circle. If the difference between the area of the circle and the area of the hexagon is 24 m^2, use the formula for the area of a sector to approximate the radius "r" of the circle.
Area of a sector = 1/2(r^2)(theta)
Can anyone work out this trig problem step by step please. This one has stumped me.
- tcLv 75 years agoFavorite Answer
A hexagon is inscribed in a circle. => the side = r
the area of hexagon = 6*(1/2 √3r/2 *r) = 3√3/2 r^2 => 6 equ. triangles
the area of circle = πr^2
πr^2 - 3√3/2 r^2 = 24
r^2(π - 3√3/2) = 24
r^2 = 24 / (π - 3√3/2)
r = 6.645 m