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# 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.

### 1 Answer

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- 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

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