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
Yuri [45]
3 years ago
10

A disk with radius 3 units is inscribed in a regular hexagon. Find the approximate area of the inscribed disk using the regular

hexagon

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
6 0

Answer:

The approximate are of the inscribed disk using the regular hexagon is A=18\sqrt{3}\ units^2

Step-by-step explanation:

we know that

we can divide the regular hexagon into 6 identical equilateral triangles

see the attached figure to better understand the problem

The approximate area of the circle is approximately the area of the six equilateral triangles

Remember that

In an equilateral triangle the interior measurement of each angle is 60 degrees

We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon

Let

M  ----> the mid-point of AB

OM ----> the perpendicular bisector of AB

x ----> the measure of angle AOM

m\angle AOM =30^o

In the right triangle OAM

tan(30^o)=\frac{(a/2)}{r}=\frac{a}{2r}\\\\tan(30^o)=\frac{\sqrt{3}}{3}

so

\frac{a}{2r}=\frac{\sqrt{3}}{3}

we have

r=3\ units

substitute

\frac{a}{2(3)}=\frac{\sqrt{3}}{3}\\\\a=2\sqrt{3}\ units

Find the area of six equilateral triangles

A=6[\frac{1}{2}(r)(a)]

simplify

A=3(r)(a)

we have

r=3\ units\\a=2\sqrt{3}\ units

substitute

A=3(3)(2\sqrt{3})\\A=18\sqrt{3}\ units^2

Therefore

The approximate are of the inscribed disk using the regular hexagon is A=18\sqrt{3}\ units^2

You might be interested in
The length of a rectangle is 2x+1 and the width is 4x-3. Write an expression to calculate the area. (Note: Area= length • width)
maw [93]
(4x-3)(2x+1) expand the brackets: 8x^2 -2x -3 = area
7 0
3 years ago
Find a slope of the line that passes through (7,-4) and (81,92)​
Leokris [45]

Answer:

48/37

Step-by-step explanation:

Use the formula (y1 - y2)/(x1 - x2).

Plug in your x and y values to get (92 + 4)/(81 - 7).

Simplify down to get 96/74 and simplify again to get 48/37.

5 0
3 years ago
NEED HELP NOWWW Which of the following is a monomial?
Dafna11 [192]

Answer: C

Step-by-step explanation:

A monomial is a expression where in it is x to the power of something, and x cannot be a denominator

4 0
3 years ago
The perimieter of parallelogram ABCD is 86cm. AD is 4cm more than twice AB. Find the length of BC.
Dafna11 [192]

Answer: 30

Step-by-step explanation: i’m not sure but my hw says it’s right

6 0
3 years ago
Latisha worked for six hours and 45 minutes how should she write that on her time card
AlexFokin [52]

Answer:

Hey there!

6 hrs 45 mins =  405 mins, or 6.75 hours.

Hope this helps :)

8 0
3 years ago
Other questions:
  • A complicated mechanical system contains 8 components. If there is a 18% chance that each component will fail during processing,
    9·1 answer
  • Help me out please<br> I need it done by Monday
    8·2 answers
  • The number of boys in a school is 120% the number of girls at the school. What is the number of boys if there are 320 girls?
    14·2 answers
  • Kevin earn 16 an hour. How much will he earn in 40 hours?
    6·2 answers
  • Lexi has 24 students in her class 2/3 of the students are girls.how many girls are in lexis class?
    10·1 answer
  • Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?
    12·2 answers
  • Each of the 25 students in Mr Walker's class sold 16 raffle tickets. If each ticket costs $15 how much money did Mr Walker's stu
    14·1 answer
  • Factor this equation<br> 4x^2+12x-7
    10·1 answer
  • ***WILL GIVE BRAINLIEST***<br> graph y= -3x +7 show picture please
    10·1 answer
  • For the following polynomial expression, find its number of terms and degree:82? y? + 327 g2 + 22y-Y.Number of terms (number val
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!