Free Printable Apothem of Regular Polygons

1.

Given Side length. What equation would you use to get the Apothem?

a)

$\frac{SideLength}{2\cdot\tan\left(\theta\right)}$

b)

$\frac{SideLength}{2\cdot\sin\left(\theta\right)}$

c)

$\frac{SideLength}{2\cdot\cos\left(\theta\right)}$

d)

$SideLength\cdot\cos\left(\theta\right)$

2.

Given Radius. What equation would you use to get the Apothem?

a)

$\frac{Radius}{\tan\left(\theta\right)}$

b)

$2\cdot Radius\cdot\sin\left(\theta\right)$

c)

$\frac{Radius}{2\cdot\cos\left(\theta\right)}$

d)

$Radius\cdot\cos\left(\theta\right)$

3.

Given Apothem. Write the equation to find the Side Length

a)

$\frac{apothem}{\tan\left(\theta\right)}$

b)

$2\cdot apothem\cdot\sin\left(\theta\right)$

c)

$2\cdot apothem\cdot\tan\left(\theta\right)$

d)

$\frac{apothem}{\cos\left(\theta\right)}$

4.

Which Segment is the APOTHEM for the figure?

a)

HM

b)

HG

c)

OG

5.

Which Segment is the Radius for the figure?

a)

HM

b)

HG

c)

OG

6.

The figure is a regular pentagon (5 sided)

The Dash line Apothem = 10

Round to the nearest hundredth place 0.00

Find the Central Angle between the Apothem and the Red Radius :

$\frac{360}{sides}\cdot\frac{1}{2}$

(a)

7.

The figure is a regular pentagon (5 sided)

The Dash line Apothem = 10

Round to the nearest hundredth place 0.00

Find the Radius :

$\frac{Apothem}{\cos\left(central\ angle\right)}$

(a)

8.

The figure is a regular pentagon (5 sided)

The Dash line Apothem = 10

Round to the nearest hundredth place 0.00

Find the length of the side :

$2\cdot apothem\cdot\tan\left(central\ angle\right)$

(a)

9.

Given ::

The figure is a regular hexagon (6 sided)

The Red line Radius = 12

Find the Central Angle between the Apothem and the Red Radius:

$\frac{360}{sides}\cdot\frac{1}{2}$

(a)

10.

Given ::

The figure is a regular hexagon (6 sided)

The Red line Radius = 12

Find the Apothem:

$Radius\cdot\cos\left(central\ angle\right)$

Round to the nearest hundredth place 0.00

(a)

11.

Given ::

The figure is a regular hexagon (6 sided)

The Red line Radius = 12

Find the Length of the Side:

$2\cdot Radius\cdot\sin\left(central\ angle\right)$

Round to the nearest hundredth place 0.00

(a)

12.

The figure is a regular decagon (10 sided)

length of Side = 25

Find Central Angle between the Apothem and the Red Radius:

$\frac{360}{sides}\cdot\frac{1}{2}$

(a)

13.

The figure is a regular decagon (10 sided)

length of Side = 25

Find Apothem

$\frac{side}{2\cdot\tan\left(central\ angle\right)}$

Round to the nearest hundredth place 0.00

(a)

14.

The figure is a regular decagon (10 sided)

length of Side = 25

Find Radius

$\frac{side}{2\cdot\sin\left(central\ angle\right)}$

Round to the nearest hundredth place 0.00

(a)

15.

Given ::

Regular Equilateral Triangle (3 sided figure)

Side = 18

Find the Apothem

a)

10.39

b)

9

c)

60

d)

5.20

16.

Given ::

The figure is a regular hexagon (6 sided)

The Red line Radius = 21

Find the Apothem:

a)

21

b)

18.19

c)

10.5

d)

15.15

Apothem of Regular Polygons

Total questions: 16

Worksheet time: 2hrs 21mins

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