Name ___________________________________________________ Date _______________
Regular Polygons Review - Geometry Honors
Find the area of the following regular polygons in simplest radical form.
1.
2.
3.
4.
5.
6.
7.
8.
Find the area of the following regular polygons. Round your answer to the nearest tenth.
9.
10.
11.
12.
octagon with radius 10 cm
13. nonagon with radius 6 ft
14. 15-gon with perimeter 120 ft
15. 18-gon with perimeter 126 m
16. 20-gon with radius 3 in.
17.
18.
Find the area of the shaded region.
19.
20.
21. What is the probability that a point randomly chosen from inside the circle would also be inside the
rectangle?
22. Your math teacher draws a regular hexagon with a circle circumscribed around it. The radius of the circle is
5 m. To the nearest tenth, what is the area of the hexagon?
23. You and your friend are playing a target game based on the board at the right (not drawn to scale). You
must hit the border to win a point. Your friend must hit the circle in the center.
a. Is the game fair? That is, do you or your friend have an equal probability of hitting your target zones?
Explain. If the game is not fair, find the radius of the circle that would make it fair.
b. Find the probability that you do not score a point.
24. Use the dartboard at the right for Exercises 14–16. Assume that a dart you throw will land on the
dartboard and is equally likely to land at any point on the board.
What is the probability of hitting region X?
What is the probability of hitting region Y?
What is the probability of hitting region Z?
25. A soccer ball’s outer covering is made by stitching together 12 regular pentagons and 20 regular hexagons.
Both polygons have a side length of 3 cm. The pentagons have an apothem of 2.06 cm. To the nearest whole
number, what is the total surface area of the soccer ball?
26. A stop sign is a regular octagon. Each side of the sign is 12.6 in. long. If you needed to cover the front and
back of the sign in a protective coating, how many square inches would you have to cover?
27. A quilter is cutting fabric for her quilt. She has several pieces of fabric from an old project that are in the
shape of regular octagons. She wants to cut the octagons into right triangles. If she divides each octagon into
16 triangles, what is the measure of the non-right angles of each triangle?
28. Several streets intersect to form triangles near Dupont Circle in Washington, D.C. One such triangle is
formed by New Hampshire Avenue, Massachusetts Avenue, and 16th Street. The section of New Hampshire
Avenue is about 3100 ft long. The section of 16th Street is about 3500 ft long. The angle enclosed by the two
streets has a measure of about 35. What is the area of this triangle, to the nearest 100 ft 2?
29. A family wants to put the tiles shown at the right in their bathroom. Each tile is a regular hexagon with a
radius of 1 in. They need to cover an area that is 48 square ft. About how many tiles do they need? Round to
the nearest whole tile.
30. A math teacher draws an equilateral triangle with radius 6 in. and a square with the same radius. Which
figure has a greater area? To the nearest tenth, how much greater is the area?