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
Leviafan [203]
3 years ago
14

A regular octagon is inscribed inside a circle. The perimeter of the octagon is units. A: What is the measure of a side of the o

ctagon? B: What is the measure of a central angle of the octagon? C: What is the approximate measure of the apothem of the octagon (to the nearest hundredth of a unit)? D: Using your answer to part C, what is the approximate area of the octagon (to the nearest whole )?

Mathematics
1 answer:
trasher [3.6K]3 years ago
7 0

Answer:

Explained below.

Step-by-step explanation:

Consider the diagram of a regular octagon is inscribed inside a circle.

Suppose the perimeter if the octagon is 8<em>a</em>.

(a)

Compute the measure of a side of the octagon as follows:

\text{Perimeter}=8\times side\\\\8\times side=8a\\\\side=a

Thus, the side of the octagon is <em>a</em> units.

(b)

The sum of all angles of around a point is 360°.

Consider the point P on the octagon.

The sum of all the angle surrounding P will be 360°.

There are a total of 8 angle surrounding the point P.

Then the measure of central angle is:

\text{Central Angle}=\frac{360^{o}}{8}=45^{o}

Thus, the measure of central angle is 45°.

(c)

The line segment from the center of an octagon to the midpoint of a side, perpendicular to said side, is known as the apothem.

Consider the diagram.

In the diagram the line segment PC is an apothem, that is perpendicular to the AB.

The measure of segment AC = a/2 and the measure of segment PA is <em>r</em> (radius of the circle).

Compute he measure of PC as follows:

PA^{2}=PC^{2}+AC^{2}\\\\PC^{2}=PA^{2}-AC^{2}\\\\PC=\sqrt{PA^{2}-AC^{2}}

      =\sqrt{r^{2}-\frac{a^{2}}{4}}

Thus, the measure of the apothem of the octagon  is\sqrt{r^{2}-\frac{a^{2}}{4}}.

(d)

The area of an octagon is:

\text{Area}=2(1+\sqrt{2})a^{2}

You might be interested in
2 1/6 + -5/6 = ? please if its a decimal please right 3.2 instead of 3.4839
Lisa [10]

Answer:

1 2/6 is the correct answer

Step-by-step explanation:

in 2 1/6 + -5/6 what you do is you can turn the plus sign into a minus sign and  make -5/6 5/6 so now the problem is 2 1/6 - 5/6 and the awnser to that is 1 2/6

4 0
3 years ago
Read 2 more answers
Explain how you can use 4S facts to solve 8×3?
Otrada [13]
8X3 equals 24
3x 8 equals 24

Eight rows of 3 =24
3 rows of 8 = 24

4 0
3 years ago
Read 2 more answers
Find the least common denominator of the two fractions from part B. To do this, list and compare the first five multiples of the
algol [13]

Answer:Find the least common denominator of the two fractions from part B. To do this, list and compare the first five multiples of the denominators. The smallest number that appears in both lists is the least common denominator. Show your work.

Step-by-step explanation:

4 0
3 years ago
Oliver traveled 124.25 miles in 3.5 hours at a constant speed. What is the constant of proportionality in miles per hour?
Elan Coil [88]

Answer:

Simple!

All you have to do is divide 3.5 by 124.25

124.25 / 3.5 = 35.5

Your answer is C.

Hope this helps!


3 0
3 years ago
Read 2 more answers
Dhruv is 24 years older than Sanjay.10 years back Dhruv’s age was five times the age of Sanjay. Find their ages.
PolarNik [594]
5x-10=24. X=24+10/5 =6.8 Sanjay age =6.8 Dhruv age, X/5 =6.8=34 Dhruv age = 34
4 0
3 years ago
Read 2 more answers
Other questions:
  • Why is y=-9x proportional?
    8·1 answer
  • Cheryl drove 4 hours at a constant rate to travel 160 miles. At what rate did she drive?
    9·2 answers
  • M=3,(-5,-3) how can i write this is slope intercept form
    12·1 answer
  • Find total weight of boxes of pecans in shipment of 3 lb boxes of pecans and 2 lb boxes of walnuts.
    11·1 answer
  • Smith chose the underlined words for a reason. What
    14·2 answers
  • Maria drove from Los Angeles (elevation 330 feet) to Death Valley (elevation –282 feet). What is the difference in elevation bet
    9·1 answer
  • Christy and Becky went apple picking.Christy picked 1/4 the amount of apples that Becky picked.If Becky picked 124 apples.how ma
    13·1 answer
  • HELP ASAP!!!! PLEASE HELP!!!!
    15·1 answer
  • 15 pts!
    15·1 answer
  • Graph (1,-3) on a grid
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!