Find the Number of Sides in a Regular Polygon Inscribed in a Circle of Radius r

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SUMMARY

A regular polygon with n sides inscribed in a circle of radius r has an area of 2r²√2. To determine the number of sides (n), one can utilize the formula for the area of a triangle, A = 1/2 * a * b * sin(C), where each triangle is formed by drawing radii to the vertices of the polygon. By calculating the area of these n triangles and equating it to the given area, the value of n can be derived. The solution involves algebraic manipulation and understanding of trigonometric functions.

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Hi guy's I am havin trouble with this problem... can anyone help me out...A regular polygon of n sides is inscribed in a circle of radius r. if the area of the polygon is 2r^2 root 2 how many sides does it have
 
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Take the polygon has n sides. Now draw radius to each vertex of the polygon. we form n triangles whose area are equal. now use the formula that the area of a triangle ABC is given by 1/2absinC.
 

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