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
grin007 [14]
3 years ago
14

Find the area of the regular polygon below. leave your answer in simplest radical form.

Mathematics
2 answers:
Licemer1 [7]3 years ago
6 0

Answer:

384√3 in²

Step-by-step explanation:

Given in the question a regular 6 sided polygon

To find it's area you have to use the following formula

<h3>      1/2 x perimeter x apothem</h3>

<em>Perimeter = the sum of the lengths of all the sides </em>

<em>Suppose length of one side = x</em>

<em>Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3</em>

<em />

Since the polygon have 6 sides so

perimeter = 6x

<h3>x = 2(8√3)/√3</h3>

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

<h3>1/2 x 96 x 8√3</h3>

384√3 in²

tamaranim1 [39]3 years ago
3 0

Answer:

= 384√3 In²

Step-by-step explanation:

The polygon is a hexagon ; thus the angle subtended by each side at the center will be given by;

θ = 360/6

 = 60°

Therefore; we can calculate the length of each side;

Tan θ = opp/Adj

Tan θ = x /8√3

 Tan 30 = x /8√3

Therefore; 1/√3 =x /8√3

x = 8√3× 1/√3

   = 8

The length of each side is 8 × 2 = 16 In

The area of the polygon will be;

Area of one triangle multiplied by the number of a triangle;

= 1/2 × 16 × 8√3 ×6

<h3><u>= 384√3 In²</u></h3>
You might be interested in
Solve for c.<br><br> a(b − c)=d<br> Attachment added
DochEvi [55]
A(b-c)=d solution is number 2. Attachment added

7 0
3 years ago
Solve this equation<br> 5x+2=3x-20-1x
Rainbow [258]
5x+2=3x-20-1x\\5x+2=2x-20\ \  \ \ |subtract\ 2\ from\ both\ sides\\5x=2x-22\ \ \ \ |subtract\ 2x\ from\ both\ sides\\3x=-22\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=-\frac{22}{3}}\Rightarrow\boxed{x=-7\frac{1}{3}}
6 0
3 years ago
Read 2 more answers
In a election about 500,000 people voted in all what could be the exact number of people who voted in the election
mariarad [96]
The best estimate would be around 350,000 to 450,000
3 0
3 years ago
I need to know what’s the the length
Monica [59]

Answer:

b=4

Step-by-step explanation:

P.T.c^2=a^2 +b^2

5^2=3^2 +b^2

25=9+b^2

b^2 =25-9

b^2 =16

b=sqrt(16)

b=4

8 0
3 years ago
Cards are drawn, one at a time, from a standard deck; each card is replaced before the next one is drawn. Let X be the number of
steposvetlana [31]

Cards are drawn, one at a time, from a standard deck; each card is replaced before the next one is drawn. Let X be the number of draws necessary to get an ace. Find E(X) is given in the following way

Step-by-step explanation:

  • From a standard deck of cards, one card is drawn. What is the probability that the card is black and a jack? P(Black and Jack)  P(Black) = 26/52 or ½ , P(Jack) is 4/52 or 1/13 so P(Black and Jack) = ½ * 1/13 = 1/26
  • A standard deck of cards is shuffled and one card is drawn. Find the probability that the card is a queen or an ace.

P(Q or A) = P(Q) = 4/52 or 1/13 + P(A) = 4/52 or 1/13 = 1/13 + 1/13 = 2/13

  • WITHOUT REPLACEMENT: If you draw two cards from the deck without replacement, what is the  probability that they will both be aces?

P(AA) = (4/52)(3/51) = 1/221.

  • WITHOUT REPLACEMENT: What is the probability that the second card will be an ace if the first card is a  king?

P(A|K) = 4/51 since there are four aces in the deck but only 51 cards left after the king has been  removed.

  • WITH REPLACEMENT: Find the probability of drawing three queens in a row, with replacement. We pick  a card, write down what it is, then put it back in the deck and draw again. To find the P(QQQ), we find the

probability of drawing the first queen which is 4/52.

  • The probability of drawing the second queen is also  4/52 and the third is 4/52.
  • We multiply these three individual probabilities together to get P(QQQ) =
  • P(Q)P(Q)P(Q) = (4/52)(4/52)(4/52) = .00004 which is very small but not impossible.
  • Probability of getting a royal flush = P(10 and Jack and Queen and King and Ace of the same suit)
5 0
3 years ago
Other questions:
  • 20/25= what percent (include explanation)
    11·1 answer
  • Explain the difference in meaning between 1-3 and -3 help help :0
    7·1 answer
  • The following polynomial has factors (x + 8) and (3x + 2). Determine the value of k. −6x^3-55x^2+kx−16
    5·1 answer
  • What is the factor of -12n - 20
    6·1 answer
  • What was the age distribution of prehistoric Native Americans? Extensive anthropological studies in the southwestern United Stat
    6·2 answers
  • Rajan bought 5 copies of a book to give as gifts. The book was on sale for $5 off the
    12·1 answer
  • For which distributions is the median the best measure of center?
    10·1 answer
  • 3/4 x 5/6 plssssssssssss help
    5·2 answers
  • Need help ASAP!!!!!<br> Will make you brainlist
    14·2 answers
  • Can somebody help me with this question. Will mark brainliest.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!