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NAME _____________________ Regular Polygon Review Sheet 1. What is the formula for each of the following ? a. Sum of the interior angles of a polygon with n - sides ? ___________________ b. Sum of the exterior angles of a polygon with n - sides ? ___________________ c. One exterior angle of a polygon with n - sides ? ___________________ d. One interior angle of a polygon with n - sides ? ___________________ 2. What is the sum of the interior angles of a polygon with 15 sides ? 3. What is the sum of the interior angles of a regular polygon whose exterior angle is 40° ? 4. What is the sum of the interior angles of a polygon with 18 sides ? 5. What is the measure of one interior angle of a polygon with 18 sides ? 6. What is the measure of one exterior angle of a polygon with 24 sides ? 7. If the sum of the interior angles is 4 times the sum of the exterior angles of a polygon, how many sides does the polygon have ? 8. What is the measure of the central angle of a regular octagon ? 9. What is the lengths of the radius, apothem, and side of a regular nonagon whose perimeter is 72 cm ? Geometry Honors Livingston High School Mr. Lamb Regular Polygons Mathematics Department 10. If a regular octagon is formed from a square, by slicing off each of the four corners, and the length of each side of the octagon is 42 cm, what is the area of the original square ? How far apart, in radical form, are the opposite sides of the square ? 11. What is the sum of the interior angles of a regular polygon if one angle of the polygon is 170° ? 12. What is the area formula, in terms of trigonometry, for the area of an n-sided polygon whose radius is R ? 13. What is the area formula, in terms of trigonometry, for the area of an n-sided polygon whose side is S ? 14. What is the area of a regular triangle whose apothem is 6 cm ? 15. What is the area of a regular hexagon whose apothem is 6 cm ? 16. What is the area of a regular triangle whose radius is 6 cm ? 17. What is the area of a regular decagon whose side is 6 cm ? 18. A regular hexagon has an area of 483 cm2 , find the apothem, radius, and perimeter. NAME _____________________ Polygon Review Sheet #2 Geometry Honors Livingston High School Mr. Lamb Regular Polygons Mathematics Department 1. What is the sum of the interior angles of a polygon with 22 sides ? 2. What is the sum of the interior angles of a regular polygon whose exterior angle is 22½° ? 3. What is the sum of the interior angles of a polygon with 45 sides ? 4. What is the measure of one interior angle of a polygon with 45 sides ? 5. What is measure of one exterior angle of a regular nonagon ? 6. What is the sum of the interior angles of a regular decagon ? 7. What is the sum of the interior angles of a regular polygon if one angle of the polygon is 160° ? 8. How many diagonals, in total, will a polygon have if the average interior angle is 167½° ? 9. Why is it impossible for a regular polygon to have an interior angle of 110° ? 10. What is the measure of one interior angle of a regular hexagon ? 11. What is the length of one side of a regular octagon whose radius is 16 cm? 12. What is the apothem of a regular octagon whose radius is 16 cm? 4 13. What is the area of a regular octagon whose radius is 16 cm? Express the answer in simplest radical form. Geometry Honors Livingston High School Mr. Lamb Regular Polygons Mathematics Department 14. The number of diagonals from a single vertex of a regular polygon is 17. What is the measure of the interior angle? What is the sum of the interior angles? 15. What is the area of a regular triangle with apothem 15 cm ? 16. What is the area of a regular hexagon with apothem 15 cm ? 17. What is the side of a regular pentagon whose radius is 20 cm? 18. What is the apothem of a regular pentagon whose radius is 20 cm? 19. What is the area of a regular pentagon whose radius is 20 cm? 20. What is the diagonal of a regular pentagon whose radius is 20 cm? 21. If six angles of an octagon are each 150, and the remaining two angles are equal, what are their measures ? 22. If five angles of a nonagon are each 124, and the remaining angles are equal, what are their measures ? 23. If three angles of an hexagon are each 118, and the remaining angles are equal, what are their measures ? Geometry Honors Livingston High School Mr. Lamb Regular Polygons Mathematics Department