1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dovator [93]
3 years ago
6

Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal

culate the exact length of the radius and the perimeter of regular hexagon ABCDEF. In your final answer, include your calculations.
Mathematics
1 answer:
Phantasy [73]3 years ago
5 0

Answer:

Part A

The \ circumradius, \  R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}

Plugging in the given values we get;

The \ circumradius, \  R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3}  \times \dfrac{2}{\sqrt{3} }  = 12

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)

Therefore;

s = 6 \cdot \sqrt{3}  \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3}  \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

a = R \cdot cos \left(\dfrac{\pi}{n} \right)

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

The \ circumradius, \  R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}

Plugging in the values gives;

The \ circumradius, \  R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3}  \times \dfrac{2}{\sqrt{3} }  = 12

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)

Therefore, we get;

s = 6 \cdot \sqrt{3}  \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3}  \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

You might be interested in
Please help me solve the first one and show all work
Leto [7]
Acc. to midpoint theorem,

15={(2x+9) + (4x-15)}/2
⇒ 30=2x+9+4x-15
⇒ 30-9+15=6x
⇒ 36/6=x
⇒6=x

WZ= 4x-15
=4*6-15
=24-15=9

3 0
3 years ago
Which is the area of a square with one side that measures 1 foot?
castortr0y [4]
None of the above so D
3 0
3 years ago
"400 reduced by 4 times my age is 116." what is his age?
Lynna [10]
400 reduced by 4 times my age is 116...

400 - 4x = 116
-4x = 116 - 400
-4x = - 284
x = -284/-4
x = 71 <===
4 0
3 years ago
Mary can run 5 kilometers in 18.75 minutes.
trasher [3.6K]

Answer:

30 minutes

Step-by-step explanation:

Find the unit rate (time per SINGLE kilometer).

5/5=1 18.75/5=3.75

Multiply 3.75 (unit rate) by 8.

3.75 x 8=30

8 0
3 years ago
Apply The axes in the coordinate grid at the right represent the walls of a bedroom. One corner of the room is at the origin. Wh
Novosadov [1.4K]

Answer: 11.2 because I know trust me. I did a worksheet with this same question and got 11.2 and it was correct.

5 0
3 years ago
Other questions:
  • A sphere has a diameter of 11 inches. What is it's surface area? Use 3.14 to approximate pie
    9·1 answer
  • What would be the order?
    11·1 answer
  • Find the inverse of f(x)= 5x-2
    8·1 answer
  • Caren is making rice and beans. She can spend no more than $10 on ingredients.
    7·1 answer
  • Omar is an avid video game player and movie watcher. He has a choice of belonging to a video club with a monthly fee of $12 and
    7·1 answer
  • Simplify by distributing<br> 7(36 – 2c + 4)
    14·1 answer
  • Can anyone help me please
    15·1 answer
  • I’m working on the subject Simple interest and need help.
    5·1 answer
  • Please help!
    10·1 answer
  • A book is 21 centimeters long, how long is this in meters?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!