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Regular Polygons

Regular Polygons Warmup


Which shape is a regular polygon?

If the sum of the interior angles in a polygon equals \(1080^\circ,\) how many sides does the polygon have? (Hint: A triangle has an interior angle sum of \(180^\circ.\) A quadrilateral has an interior angle sum of \(360^\circ.\) A pentagon has an interior angle sum of \(540^\circ.\))

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. \(a, b, c,\) and \(d\) represent the areas of those regions between the circles. What is \(a + b + c + d?\)

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


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