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
deff fn [24]
3 years ago
9

Regular hexagon ABCDEF has a perimeter of 36. O is the center of the hexagon and of circle O. Circles A, B, C, D, E, and F have

centers at A, B, C, D, E, and F, respectively. If each circle is tangent to the two circles adjacent to it and to circle O, what is the area of the shaded region (inside the hexagon but outside the circles)?A. \(108-18\pi\)B. \(54\sqrt{3}-9\pi\)C. \(54\sqrt{3}-18\pi\)D. \(108-27\pi\)E. \(54\sqrt{3}-27\pi\)

Mathematics
1 answer:
morpeh [17]3 years ago
4 0

Answer:

E. (54\sqrt{3}-27\pi\)

Step-by-step explanation:

I draw the figure described by the statement down there so you can see easily how to solve it.

Notice 3 things:

- The length of one side of the hexagon is simply 36 divided by 6. = 6 This is beacause, by nature, every single side of the hexagon has the same length.

- The radius of each circle is half the length of one side of the hexagon. This would mean that the radius of each circle is 3.

- The outer circles have 120°/360° of its area enclose. We get this value because by definition, the hexagon can be divided into 6 regular triangles, each one with every angle equal to 60°. The size of the internal angles of the hexagon will be twice this value.

So, in summary, The area enclosed by the circles is expressed like this:

Acircles = 6 * \frac{120}{360} * π * (r)² + π*r² = 3 * π * r² = 27 π

Now all we need is the area of the regular hexagon, which is simply:

Ahexagon = \frac{1}{2}* p * a

Where p is the perimeter, given by the problem, and a is its apothem, the distance between the center of the hexagon and the middle of one of its sides, that is found by multiplying the length of a side of the hexagon times \frac{\sqrt{3}}{2}.

Ahexagon = \frac{1}{2} * 36 * 6 * \frac{\sqrt{3}}{2} = 54\sqrt{3}.

Then, the area of the shaded area is equal to:

Ashaded = Ahexagon - Acircles = 54\sqrt{3} - 27π

You might be interested in
L 3.1.4 Quiz: Limits Practice Consider the following graph of y= f(x): n 2 2 0 What is the lim f(x)? A. 1 O B. 2 O c. C. - 2 D.
loris [4]

Answer:

0

I would appreciate if my answer is chosen as a brainliest answer

5 0
2 years ago
Find the area of an equilateral triangle with side length 9.2 cm. Round your answer to 1 DP.
lbvjy [14]

Answer:

Area=36.66 cm^2

Step-by-step explanation:

First, you need the height.

Use the Pythagorean theorem:

hypotenuse^2=height^2+(1/2 base)^2  

It's one-half base because it's an equilateral triangle.

1/2 base =4.6

(9.2)^2-4.6^2=height^2

84.64-21.16=height^2

height^2=63.48

height=7.97

Area=(1/2)(base)(height)

Area=(1/2)(9.2)(7.97)=36.66 cm^2

3 0
3 years ago
Cate and elena were playing cards
Delicious77 [7]
There were...
11cards left.
heres why.
they started with 24 cards....
so...
24+8=32
32-12=20
20-9=11

Hope i helped!!! :)
Mark me as brainliest if i helped XD
6 0
3 years ago
WILL MARK YOU BRAINLIEST
spayn [35]
I34 hope that helps
4 0
3 years ago
PLEASE HELP
nirvana33 [79]

You don't say whether this is a right triangle or not.

Assuming it is a right triangle, then we use the Pythagorean Theorem to determine the length of the hypotenuse:

(hypo) = (length of third side) = √(12^2 + 4^2) = √(144+16) = √160 = 4√10.

This is approx. 12.65 inches. Since this does not match any of the possible answer choices, we'll have to take a different approach to answering this question.

Given that 2 sides of the given triangle are 12 and 4 inches, respectively, we see that the 3rd side has to be longer than 8 inches; otherwise we'd have three line segments on the same line, not forming a triangle.

By this reasoning, 9 inches is the only possible answer that could be correct. With sides 12, 9 and 4 inches, the triangle would be obtuse and appear quite flat, but not be part of a straight line as with a third side of 8.


6 0
3 years ago
Other questions:
  • At a store, hot dogs come in packages of eight and hot dog buns come in packages of twelve. What is the least number of packages
    8·1 answer
  • The area of a rectangle is 28square miles. The length is 7 miles.
    6·1 answer
  • James has a job with a current salary of $42,000. He wants to earn a college degree that will take him 2 years to complete and i
    7·2 answers
  • Can any one help me answer this Math question ?
    8·1 answer
  • Henry can write 5pages of his novel in 3 hours.
    12·2 answers
  • Michael picks three different digits from the set { } 12345 ,,,, and forms a mixed number by placing the digits in the spaces of
    10·1 answer
  • Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both
    9·1 answer
  • I dont know how i would put this question without useing photos
    15·1 answer
  • What is the solution to the equation g(x+2) = 27? (1 point)
    14·2 answers
  • Mary and Jane both took PSY230 last semester but they were in two different sections taught by different professors. Mary's clas
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!