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# NAME Polygon Review Sheet _3 by malj

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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 42 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

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 483 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?

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13. What is the area of a regular octagon whose radius is 16 cm? Express the answer in

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

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