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
Starting from the origin, how is point ( – 5, 4) plotted?
Feliz [49]
It’s gonna be 5 units left and 4 units up. Because 5 is going negative in the x axis and 4 is going positive in the y axis
8 0
3 years ago
Find the balance in the account after the given period. ​$2000 principal earning 6​% compounded​ annually, for 8 years. The bala
Harman [31]
Do 2000 divided by 8 than divided that by 6%
8 0
3 years ago
Read 2 more answers
Sonia opened a savings account and then added the same amount to the savings account eyery week. After 5 weeks, her savings acco
Goryan [66]

Answer:

since Sonia saved 45$ in 5 weeks and 70$ in 10 weeks. we are to find the amount she saved up in x weeks.

let's make the amount y

so x= y

5 = 45 cross multiplying the values

we then have 45x= 5y

y= 7x

x=y

10=70

10x = 70y

y= 7x = y=5x+ 20, y = 20x+5

7 0
3 years ago
Find the value of x.
faust18 [17]

Answer:

          7 sqrt(3) =x

Step-by-step explanation:

We know that sin 60 = opposite / hypotenuse

                       sin 60 = x/14

Multiply both sides by 14

                          14 sin 60 = x

                        14 * (sqrt(3)/2) =x

                      7 sqrt(3) =x

8 0
3 years ago
Read 2 more answers
15 quarters to 3 dollars<br>​
Anarel [89]

Answer:

so, it's 3.75 to 3

Step-by-step explanation:

15 quarters is 3 dollars and 3 quarters

4 0
2 years ago
Other questions:
  • I'm having trouble with this<br><br> -9x + 4y = 55<br> -11x + 7y = 82
    12·2 answers
  • What are the subsets of (1, 5, 9)
    12·2 answers
  • Am I on the right track for #16? If not plz explain. What are the next steps?
    13·1 answer
  • Hey I have a link to the question since its kinda complicated
    8·2 answers
  • If sales tax is 7%, what would the tax on. $7.99 meal be? What would the meal cost after tax?
    5·2 answers
  • What is the exact value of cos 112.5°?
    15·1 answer
  • Kyle is going to the County Fair with his friends. It
    15·1 answer
  • Someone please help me with this ASAP
    5·2 answers
  • PLZ Help Urgent. 15 POINTS, BRAINLY Guaranteed.
    6·2 answers
  • Maths ACSF<br>1.5 m<br>2500 mm<br>850 <br>4.8m <br>whats the total length <br>​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!