Regular Polygons

Regular Polygons Warmup


Which shape is a regular polygon?

If the sum of the interior angles in a polygon equals 1080,1080^\circ, how many sides does the polygon have? (Hint: A triangle has an interior angle sum of 180.180^\circ. A quadrilateral has an interior angle sum of 360.360^\circ. A pentagon has an interior angle sum of 540.540^\circ.)

A hexagon is inscribed in a circle with a radius of 6. What is the area of the hexagon?

Nine identical circles are placed adjacent to one another in three rows in a square whose area is 9. a,b,c,a, b, c, and dd represent the areas of those regions between the circles. What is a+b+c+d?a + b + c + d?

An angle is formed by extending two sides of a regular heptagon, as shown. What is the closest approximate value of x?x?


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