Geometry

Regular Polygons

Regular Polygons - Properties of Regular Polygons

         

The above diagram shows 33 identical regular hexagons with side length 7.7. If O1,O2O_{1}, O_{2} and O3O_{3} are their respective centers, what is the area of O1O2O3?\triangle O_{1}O_{2}O_{3}?

The above diagram is part of a regular polygon with nn sides whose center of gravity is O.O. If n=10n=10 and the length of a side of the polygon is 30,30, what is the ratio of the areas of the inscribed circle and circumscribed circle?

The above diagram is a triangular prism whose faces are all regular polygons. If the length of AB\overline{AB} is 3, 3, what is the volume of the triangular prism?

The length of each side in the above regular octagon is 8.8. What is its area?

If each of the angles in a regular polygon is 120120^{\circ}, how many vertices does this polygon have?

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