Regular Polygons

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Show your work for each problem.

1.
Which of these shapes is a regular polygon?
1. a)A right triangle
2. b)A rectangle 4 cm by 7 cm
3. c)A square
4. d)A rhombus with angles of $60°$ and $120°$
2.
What is each exterior angle of a regular decagon (10 sides), in degrees?
3.
Find each interior angle of a regular pentagon.
4.
What is each interior angle of a regular hexagon?
1. a) $120°$
2. b) $108°$
3. c) $60°$
4. d) $720°$
5.
A regular octagon has sides of 7 cm. What is its perimeter in cm?
6.
A regular nonagon has 9 sides. Find its exterior angle and then its interior angle.
7.
Which regular polygon can tile a floor on its own, with no gaps and no overlaps?
1. a)Regular hexagon
2. b)Regular pentagon
3. c)Regular decagon
4. d)Regular octagon
8.
What is each interior angle of a regular 12-sided polygon (dodecagon), in degrees?
9.
A regular hexagon with sides of 5 cm is cut into 6 triangles from its center. Find the angles of one triangle and the radius of the hexagon.
10.
The central angle of a regular polygon is $30°$ . How many sides does it have?
1. a) $12$
2. b) $9$
3. c) $6$
4. d) $10$
11.
Each interior angle of a regular polygon is $140°$ . How many sides does it have?
12.
Each interior angle of a regular polygon is $156°$ . How many sides does it have?
13.
A regular octagon has sides of 10 cm and an apothem of 12.07 cm. Find its area.
14.
A regular hexagon has sides of 4 cm. How long is its apothem?
1. a) $2\sqrt{3} \approx 3.46$ cm
2. b) $2$ cm
3. c) $8$ cm
4. d) $4$ cm
15.
A regular pentagon has a perimeter of 60 cm and an apothem of 8.26 cm. What is its area in cm²?
16.
A regular hexagon has sides of 8 cm. Find its area by splitting it into 6 equilateral triangles.
17.
Can regular octagons tile a floor on their own? Place whole octagons around one corner point and find the gap that is left, in degrees.
18.
In a regular polygon, each interior angle is 4 times as large as each exterior angle. How many sides does it have?